Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 7/2019, Volume 113, Issue 3, pp. 2479 - 2493

In this article, we construct a crystallization of the mapping torus of some (PL) homeomorphisms $$f:M \rightarrow M$$ f : M → M for a certain class of...

PL-manifolds | Crystallizations | Theoretical, Mathematical and Computational Physics | Mathematics | 57N13 | Mapping torus | 57N10 | 57Q05 | Primary 57Q15 | 57N15 | 55R10 | Gem-complexity | Mathematics, general | Regular genus | Applications of Mathematics | Secondary 05C15 | MATHEMATICS | Toruses | Mapping | Topology | Upper bounds | Crystallization | Complexity | Mathematics - Geometric Topology

PL-manifolds | Crystallizations | Theoretical, Mathematical and Computational Physics | Mathematics | 57N13 | Mapping torus | 57N10 | 57Q05 | Primary 57Q15 | 57N15 | 55R10 | Gem-complexity | Mathematics, general | Regular genus | Applications of Mathematics | Secondary 05C15 | MATHEMATICS | Toruses | Mapping | Topology | Upper bounds | Crystallization | Complexity | Mathematics - Geometric Topology

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 4/2018, Volume 288, Issue 3, pp. 829 - 853

We prove a structure theorem for closed topological manifolds of cohomogeneity one; this result corrects an oversight in the literature. We complete the...

57M60 | 57S25 | Cohomogeneity one | Group action | Smoothing | 57S10 | 57N15 | Mathematics, general | Topological manifold | Mathematics | 57R10 | LOW DIMENSIONS | SPACES | SPHERES | CLASSIFICATION | FORMULA | MATHEMATICS | INDEX | POSITIVE RICCI CURVATURE | GEOMETRY | Algebra

57M60 | 57S25 | Cohomogeneity one | Group action | Smoothing | 57S10 | 57N15 | Mathematics, general | Topological manifold | Mathematics | 57R10 | LOW DIMENSIONS | SPACES | SPHERES | CLASSIFICATION | FORMULA | MATHEMATICS | INDEX | POSITIVE RICCI CURVATURE | GEOMETRY | Algebra

Journal Article

Algebraic and Geometric Topology, ISSN 1472-2747, 04/2018, Volume 18, Issue 4, pp. 2131 - 2149

Motivated by a recent paper of Gabai (J. Topol. 4 (2011) 529-534) on the Whitehead contractible 3-manifold, we investigate contractible manifolds M-n which...

Mazur manifold | Dunce hat | Jester’s manifold | Jester’s hat | Pseudohandle | MATHEMATICS | Mathematics - Geometric Topology

Mazur manifold | Dunce hat | Jester’s manifold | Jester’s hat | Pseudohandle | MATHEMATICS | Mathematics - Geometric Topology

Journal Article

Topology and its Applications, ISSN 0166-8641, 10/2019, Volume 266, p. 106842

This paper provides further investigation of the concept of shape msimpl-fibrators (previously introduced by the author). The main results identify shape...

Manifold homotopicaly determined by [formula omitted] | Approximate fibration | Shape [formula omitted]-fibrator | Coperfectly Hopfian group | Manifold homotopicaly determined by pi | MATHEMATICS | DECOMPOSITIONS | MATHEMATICS, APPLIED | SURFACE | MANIFOLDS | Shape m(simpl)o-fibrator | APPROXIMATE FIBRATIONS | Mathematics - Geometric Topology

Manifold homotopicaly determined by [formula omitted] | Approximate fibration | Shape [formula omitted]-fibrator | Coperfectly Hopfian group | Manifold homotopicaly determined by pi | MATHEMATICS | DECOMPOSITIONS | MATHEMATICS, APPLIED | SURFACE | MANIFOLDS | Shape m(simpl)o-fibrator | APPROXIMATE FIBRATIONS | Mathematics - Geometric Topology

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 10/2014, Volume 172, Issue 1, pp. 121 - 134

This paper concerns the topology of configuration spaces of linkages whose underlying graph is a single cycle. Assume that the edge lengths are such that there...

Geometry | 70B15 | Linkage | 57N15 | Closed chain | Mathematics | Polygon | Configuration space | 55R80 | MATHEMATICS

Geometry | 70B15 | Linkage | 57N15 | Closed chain | Mathematics | Polygon | Configuration space | 55R80 | MATHEMATICS

Journal Article

Formalized Mathematics, ISSN 1426-2630, 06/2014, Volume 22, Issue 2, pp. 179 - 186

Let us recall that a topological space is a topological manifold if is second-countable Hausdorff and locally Euclidean, i.e. each point has a neighborhood...

boundary | 57N15 | 03B35 | locally Euclidean spaces | Cartesian product | interior

boundary | 57N15 | 03B35 | locally Euclidean spaces | Cartesian product | interior

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2014, Volume 66, Issue 4, pp. 1227 - 1248

In this paper we deduce a local deformation lemma for uniform embeddings in a metric covering space over a compact manifold from the deformation lemma for...

Group of uniform homeomorphisms | Space of uniform embeddings | Uniform topology | Euclidean ends | MATHEMATICS | group of uniform homeomorphisms | uniform topology | space of uniform embeddings

Group of uniform homeomorphisms | Space of uniform embeddings | Uniform topology | Euclidean ends | MATHEMATICS | group of uniform homeomorphisms | uniform topology | space of uniform embeddings

Journal Article

Manuscripta mathematica, ISSN 1432-1785, 2014, Volume 145, Issue 3-4, pp. 433 - 448

For a given class $${\mathcal{G}}$$ G of groups, a 3-manifold M is of $${\mathcal{G}}$$ G -category $${\leq k}$$ ≤ k if it can be covered by k open subsets...

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 57N15 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 57N13 | 57M30 | 57N10 | TOPOLOGY | MATHEMATICS | FUNDAMENTAL-GROUPS | PL INVOLUTIONS | FIXED-POINTS

Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | 57N15 | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | 57N13 | 57M30 | 57N10 | TOPOLOGY | MATHEMATICS | FUNDAMENTAL-GROUPS | PL INVOLUTIONS | FIXED-POINTS

Journal Article

Tokyo Journal of Mathematics, ISSN 0387-3870, 12/2014, Volume 37, Issue 2, pp. 385 - 403

In this paper, we construct round fold maps or stable fold maps with singular value sets of concentric spheres introduced by the author [11] on smooth bundles...

Fold maps. Differential topology | Singular sets | Singularities of differentiable maps | TOPOLOGY | MATHEMATICS | fold maps | SPECIAL GENERIC MAPS | EUCLIDEAN SPACES | Differential topology | PLANE | singular sets | MAPPINGS | MANIFOLDS | 57R45 | 57N15

Fold maps. Differential topology | Singular sets | Singularities of differentiable maps | TOPOLOGY | MATHEMATICS | fold maps | SPECIAL GENERIC MAPS | EUCLIDEAN SPACES | Differential topology | PLANE | singular sets | MAPPINGS | MANIFOLDS | 57R45 | 57N15

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 6/2012, Volume 271, Issue 1, pp. 167 - 173

A closed topological n-manifold M n is of S 1-category 2 if it can be covered by two open subsets W 1, W 2 such that the inclusions W i → M n factor...

Lusternik–Schnirelmann category | Coverings of n -manifolds with open S 1 -contractible subsets | 57N15 | Mathematics, general | Mathematics | 57N13 | 57M30 | 57N10 | Lusternik-Schnirelmann category | contractible subsets | Coverings of n-manifolds with open S | MATHEMATICS | MAPS | FUNDAMENTAL-GROUPS | Coverings of n-manifolds with open S-1-contractible subsets

Lusternik–Schnirelmann category | Coverings of n -manifolds with open S 1 -contractible subsets | 57N15 | Mathematics, general | Mathematics | 57N13 | 57M30 | 57N10 | Lusternik-Schnirelmann category | contractible subsets | Coverings of n-manifolds with open S | MATHEMATICS | MAPS | FUNDAMENTAL-GROUPS | Coverings of n-manifolds with open S-1-contractible subsets

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2010, Volume 266, Issue 4, pp. 783 - 788

A closed topological n-manifold M n is of S 1-category 2 if it can be covered by two open subsets W 1, W 2 such that the inclusions W i → M n factor...

Lusternik–Schnirelmann category | Coverings of n -manifolds with open S 1 -contractible subsets | 57N15 | Mathematics, general | Mathematics | 57N13 | 57M30 | 57N10 | MATHEMATICS | Lusternik-Schnirelmann category | CATEGORY | Coverings of n-manifolds with open S-1-contractible subsets

Lusternik–Schnirelmann category | Coverings of n -manifolds with open S 1 -contractible subsets | 57N15 | Mathematics, general | Mathematics | 57N13 | 57M30 | 57N10 | MATHEMATICS | Lusternik-Schnirelmann category | CATEGORY | Coverings of n-manifolds with open S-1-contractible subsets

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 5/2013, Volume 10, Issue 2, pp. 1101 - 1106

We show that if G is an upper semicontinuous decomposition $${\mathbb {R}^n, n \ge 4}$$ , into convex sets, then the quotient space $${\mathbb {R}^n/G}$$ is a...

general position property | generalized manifold | Upper semicontinuous decomposition | Mathematics | cell-like resolution | codimension 1 manifold factor | 57N75 | convex set | Secondary 57P99 | Primary 57N15 | Generalized Moore Problem | Mathematics, general | 53C70

general position property | generalized manifold | Upper semicontinuous decomposition | Mathematics | cell-like resolution | codimension 1 manifold factor | 57N75 | convex set | Secondary 57P99 | Primary 57N15 | Generalized Moore Problem | Mathematics, general | 53C70

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 10/2010, Volume 148, Issue 1, pp. 205 - 243

Consider the cyclic group C 2 of order two acting by complex-conjugation on the unit circle S 1. The main result is that a finitely dominated manifold W of...

Geometry | 57N15 | Mathematics | Manifold approximate fibration | 57S30 | Wrapping up | Equivariant sucking | MATHEMATICS | HOMEOMORPHISMS | TOPOLOGICAL MANIFOLDS | HILBERT-CUBE MANIFOLDS | MAPS | SPACES | OBSTRUCTION | Mathematics - Geometric Topology

Geometry | 57N15 | Mathematics | Manifold approximate fibration | 57S30 | Wrapping up | Equivariant sucking | MATHEMATICS | HOMEOMORPHISMS | TOPOLOGICAL MANIFOLDS | HILBERT-CUBE MANIFOLDS | MAPS | SPACES | OBSTRUCTION | Mathematics - Geometric Topology

Journal Article

Journal of differential geometry, ISSN 0022-040X, 1988, Volume 27, Issue 1, pp. 67 - 80

Journal Article

Central European Journal of Mathematics, ISSN 1895-1074, 11/2013, Volume 11, Issue 11, pp. 1932 - 1948

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We...

Totally wild flow | Probability Theory and Stochastic Processes | Piecewise disjoint arc-disk property | Mathematics | 57P99 | Fuzzy ribbons property | 57N75 | Codimension one manifold factor | 0-stitched disks | Algebra | Generalized Moore Problem | 57N15 | Crinkled ribbons property | Disjoint homotopies property | Mathematics, general | General position | Topological Groups, Lie Groups | δ -fractured maps | Disjoint topographies property | Ghastly generalized manifold | Fractured maps property | Geometry | Plentiful 2-manifolds property | Disjoint concordances | Number Theory | 53C70 | δ-fractured maps | HOMOTOPIES PROPERTY | COLLECTIONS | delta-fractured maps | MATHEMATICS | DECOMPOSITIONS | CONTINUA

Totally wild flow | Probability Theory and Stochastic Processes | Piecewise disjoint arc-disk property | Mathematics | 57P99 | Fuzzy ribbons property | 57N75 | Codimension one manifold factor | 0-stitched disks | Algebra | Generalized Moore Problem | 57N15 | Crinkled ribbons property | Disjoint homotopies property | Mathematics, general | General position | Topological Groups, Lie Groups | δ -fractured maps | Disjoint topographies property | Ghastly generalized manifold | Fractured maps property | Geometry | Plentiful 2-manifolds property | Disjoint concordances | Number Theory | 53C70 | δ-fractured maps | HOMOTOPIES PROPERTY | COLLECTIONS | delta-fractured maps | MATHEMATICS | DECOMPOSITIONS | CONTINUA

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 6/2008, Volume 259, Issue 2, pp. 419 - 432

A closed topological n-manifold M n is of S 1-category 2 if it can be covered by two open subsets W 1,W 2 such that the inclusions W i → M n factor...

Coverings of n -manifolds with open S 1 -contractible subsets | 57N15 | Mathematics, general | Lusternik-Schnirelmann category | Mathematics | 57N13 | 57M30 | 57N10 | contractible subsets | Coverings of n-manifolds with open S | MATHEMATICS | 3-MANIFOLDS | coverings of n-manifolds with open S-1-contractible subsets

Coverings of n -manifolds with open S 1 -contractible subsets | 57N15 | Mathematics, general | Lusternik-Schnirelmann category | Mathematics | 57N13 | 57M30 | 57N10 | contractible subsets | Coverings of n-manifolds with open S | MATHEMATICS | 3-MANIFOLDS | coverings of n-manifolds with open S-1-contractible subsets

Journal Article

Central European Journal of Mathematics, ISSN 1895-1074, 6/2012, Volume 10, Issue 3, pp. 857 - 862

We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid...

Topological Groups, Lie Groups | Upper semicontinuous decomposition | ANR | Probability Theory and Stochastic Processes | Mathematics | 57P99 | Rigidity | Cell-like resolution | 57N75 | Geometry | Algebra | 57N15 | k -homogeneity | Generalized manifold | Mathematics, general | Number Theory | 53C70 | General position property | Manifold recognition theorem | k-homogeneity | MATHEMATICS | PRODUCTS | SQUARES | DIMENSIONAL COMPACTA | ARCS

Topological Groups, Lie Groups | Upper semicontinuous decomposition | ANR | Probability Theory and Stochastic Processes | Mathematics | 57P99 | Rigidity | Cell-like resolution | 57N75 | Geometry | Algebra | 57N15 | k -homogeneity | Generalized manifold | Mathematics, general | Number Theory | 53C70 | General position property | Manifold recognition theorem | k-homogeneity | MATHEMATICS | PRODUCTS | SQUARES | DIMENSIONAL COMPACTA | ARCS

Journal Article

Michigan Mathematical Journal, ISSN 0026-2285, 1998, Volume 45, Issue 3, pp. 419 - 440

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 6/2005, Volume 145, Issue 2, pp. 95 - 96

We give an easy proof of a result in [1] generalizing the well-known Borsuk’s non-retraction theorem.

Mathematics, general | Mathematics | Retraction, Borsuk’s Theorem | 2000 Mathematics Subject Classifications: 54C15, 57N15 | Borsuk's Theorem | Retraction | MATHEMATICS | retraction | Borsuk's theorem

Mathematics, general | Mathematics | Retraction, Borsuk’s Theorem | 2000 Mathematics Subject Classifications: 54C15, 57N15 | Borsuk's Theorem | Retraction | MATHEMATICS | retraction | Borsuk's theorem

Journal Article

Journal of Differential Geometry, ISSN 0022-040X, 1987, Volume 25, Issue 3, pp. 297 - 326

Journal Article

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