Glasgow mathematical journal, ISSN 0017-0895, 09/2019, Volume 61, Issue 3, pp. 727 - 742

In this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2...

Primary 57S25 | Secondary 55R20 | 57S10 | 1991 Mathematics Subject Classification | 55M20 | BORSUK-ULAM | MATHEMATICS | ORBIT SPACES | FREE INVOLUTIONS | THEOREMS | PRODUCT | Manifolds | Lower bounds | Homology | Euclidean geometry | Mathematics - Algebraic Topology

Primary 57S25 | Secondary 55R20 | 57S10 | 1991 Mathematics Subject Classification | 55M20 | BORSUK-ULAM | MATHEMATICS | ORBIT SPACES | FREE INVOLUTIONS | THEOREMS | PRODUCT | Manifolds | Lower bounds | Homology | Euclidean geometry | Mathematics - Algebraic Topology

Journal Article

Osaka J. Math, 2010, Volume 47, Issue no. 1, pp. 237 - 283

Journal Article

Topology and its applications, ISSN 0166-8641, 2018, Volume 249, pp. 112 - 126

We describe a unified approach to estimating the dimension of f−1(A) for any G-equivariant map f:X→Y and any closed G-invariant subset A⊆Y in terms of...

Coincidence set | Bourgin–Yang theorem | Cohomological length | Borsuk–Ulam theorem | Equivariant map | Representation sphere | BORSUK-ULAM | MATHEMATICS | MATHEMATICS, APPLIED | Borsuk-Ulam theorem | Bourgin-Yang theorem | Mathematics - Algebraic Topology

Coincidence set | Bourgin–Yang theorem | Cohomological length | Borsuk–Ulam theorem | Equivariant map | Representation sphere | BORSUK-ULAM | MATHEMATICS | MATHEMATICS, APPLIED | Borsuk-Ulam theorem | Bourgin-Yang theorem | Mathematics - Algebraic 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

Forum Mathematicum, ISSN 0933-7741, 11/2014, Volume 26, Issue 6, pp. 1611 - 1628

The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between shape properties of topological spaces, modeled...

Morse function | 54C30 | 57S05 | measuring function | 57S10 | size theory | 68U05 | Natural pseudo-distance | Measuring function | Size theory | TOPOLOGY | MATHEMATICS, APPLIED | DISTANCE | SPACES | SHAPES | OPTIMAL CORRESPONDENCES | PLANE-CURVES | MATHEMATICS | SIZE FUNCTIONS

Morse function | 54C30 | 57S05 | measuring function | 57S10 | size theory | 68U05 | Natural pseudo-distance | Measuring function | Size theory | TOPOLOGY | MATHEMATICS, APPLIED | DISTANCE | SPACES | SHAPES | OPTIMAL CORRESPONDENCES | PLANE-CURVES | MATHEMATICS | SIZE FUNCTIONS

Journal Article

Duke mathematical journal, ISSN 0012-7094, 1991, Volume 62, Issue 2, pp. 417 - 451

Journal Article

Annals of the Alexandru Ioan Cuza University - Mathematics, ISSN 1221-8421, 11/2014, Volume 60, Issue 2, pp. 293 - 308

In this paper, the author calculates the number of equivariant home-omorphism classes of (orientable) small covers over the product of 3-sided prism with...

57S25 | equivariant homeomorphism | 57S10 | polytope | 52B11 | small cover | Equivariant homeomorphism | Polytope | Small cover | MATHEMATICS | NUMBER | ORIENTABLE SMALL COVERS | CUBES | POLYTOPES | 2-TORUS MANIFOLDS

57S25 | equivariant homeomorphism | 57S10 | polytope | 52B11 | small cover | Equivariant homeomorphism | Polytope | Small cover | MATHEMATICS | NUMBER | ORIENTABLE SMALL COVERS | CUBES | POLYTOPES | 2-TORUS MANIFOLDS

Journal Article

数学年刊：B辑英文版, ISSN 0252-9599, 2016, Volume 37, Issue 3, pp. 331 - 356

A small cover is a closed manifold M^n with a locally standard （Z2）^n-action such that its orbit space is a simple convex polytope P^n. Let A^n denote an...

凸多面体 | 覆盖 | N2 | 等价类 | 乘积空间 | 轨道空间 | n维单形 | 流形 | Equivariant homeomorphism | Polytope | 57S25 | Small cover | 57S10 | 52B11 | Mathematics, general | Mathematics | Applications of Mathematics | 52B70 | (ℤ 2 ) n -Action | ) | Action | ℤ | MATHEMATICS | POLYTOPES | (Z)(n)-Action | Information science

凸多面体 | 覆盖 | N2 | 等价类 | 乘积空间 | 轨道空间 | n维单形 | 流形 | Equivariant homeomorphism | Polytope | 57S25 | Small cover | 57S10 | 52B11 | Mathematics, general | Mathematics | Applications of Mathematics | 52B70 | (ℤ 2 ) n -Action | ) | Action | ℤ | MATHEMATICS | POLYTOPES | (Z)(n)-Action | Information science

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 9/2013, Volume 50, Issue 2, pp. 509 - 519

The real solutions to a system of sparse polynomial equations may be realized as a fiber of a projection map from a toric variety. When the toric variety is...

Computational Mathematics and Numerical Analysis | Real toric variety | Order polytope | 57S10 | Polynomial system | 14M25 | 14P99 | Mathematics | 57B20 | Combinatorics | MATHEMATICS | POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | SCHUBERT CALCULUS | Geometry | Algebra | Lower bounds | Computational geometry | Mathematical analysis | Projection | Mathematical models | Polynomials | Fibers

Computational Mathematics and Numerical Analysis | Real toric variety | Order polytope | 57S10 | Polynomial system | 14M25 | 14P99 | Mathematics | 57B20 | Combinatorics | MATHEMATICS | POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | SCHUBERT CALCULUS | Geometry | Algebra | Lower bounds | Computational geometry | Mathematical analysis | Projection | Mathematical models | Polynomials | Fibers

Journal Article

Algebraic and Geometric Topology, ISSN 1472-2747, 01/2013, Volume 12, Issue 4, pp. 2299 - 2316

We define and study an equivariant version of Farber's topological complexity for spaces with a given compact group action. This is a special case of the...

MATHEMATICS | ROBOT MOTION | LUSTERNIK-SCHNIRELMANN | CATEGORY | Mathematics - Algebraic Topology

MATHEMATICS | ROBOT MOTION | LUSTERNIK-SCHNIRELMANN | CATEGORY | Mathematics - Algebraic Topology

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 2011, Volume 24, Issue 10, pp. 1654 - 1657

The Hausdorff distance, the Gromov–Hausdorff, the Fréchet and the natural pseudo-distance are instances of dissimilarity measures widely used in shape...

Space of homeomorphisms | Correspondence | Compact metric space | MATHEMATICS, APPLIED | Topology | Metric space | Mathematical analysis | Automorphisms | Expansion | Images

Space of homeomorphisms | Correspondence | Compact metric space | MATHEMATICS, APPLIED | Topology | Metric space | Mathematical analysis | Automorphisms | Expansion | Images

Journal Article

Proceedings of the Japan Academy Series A: Mathematical Sciences, ISSN 0386-2194, 06/2010, Volume 86, Issue 6, pp. 97 - 100

Proc. Japan Acad., 86, Ser. A (2010), 97--100 We count orientable small covers over cubes. We also get estimates for $O_n/R_n$, where $O_n$ is the number of...

Toric Topology | Real Bott manifold | Acyclic digraph | Orientable small cover | Mathematics - Geometric Topology | 57S10 | 37F20 | real Bott manifold | 57N99 | acyclic digraph

Toric Topology | Real Bott manifold | Acyclic digraph | Orientable small cover | Mathematics - Geometric Topology | 57S10 | 37F20 | real Bott manifold | 57N99 | acyclic digraph

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 8/2011, Volume 61, Issue 4, pp. 653 - 656

We show that the inverse limit and the orbit map commute for actions of compact groups on compact Hausdorff spaces.

Secondary 57S10, 54B15 | inverse limit | orbit space | Algebra | Mathematics, general | Mathematics | Primary 54B25 | equivariant map | group action | MATHEMATICS | Mathematics - General Topology

Secondary 57S10, 54B15 | inverse limit | orbit space | Algebra | Mathematics, general | Mathematics | Primary 54B25 | equivariant map | group action | MATHEMATICS | Mathematics - General Topology

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 3/2016, Volume 55, Issue 2, pp. 373 - 409

Persistent homology has proven itself quite efficient in the topological and qualitative comparison of filtered topological spaces, when invariance with...

Secondary 47H09 | Computational Mathematics and Numerical Analysis | Group action | Filtering function | Shape comparison | Mathematics | 68U05 | Natural pseudo-distance | 54H15 | 57S10 | Primary 55N35 | Combinatorics | 65D18 | Persistent homology group | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | SIZE FUNCTIONS | Geometry | Topology | Operators | Mathematical analysis | Group theory | Homology | Affinity | Mathematical models | Invariance

Secondary 47H09 | Computational Mathematics and Numerical Analysis | Group action | Filtering function | Shape comparison | Mathematics | 68U05 | Natural pseudo-distance | 54H15 | 57S10 | Primary 55N35 | Combinatorics | 65D18 | Persistent homology group | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | SIZE FUNCTIONS | Geometry | Topology | Operators | Mathematical analysis | Group theory | Homology | Affinity | Mathematical models | Invariance

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2003, Volume 131, Issue 10, pp. 3275 - 3283

Let G=S^1, G=\mathbb{Z}/p or more generally G be a finite p-group, where p is an odd prime. If G acts on a space whose cohomology ring fulfills Poincaré...

Mathematical manifolds | Mathematical theorems | Algebra | Logical proofs | Mathematical duality | Polynomials | Mathematical congruence | Coefficients | College mathematics | Induction assumption | Group action | Poincaré duality space | Betti number | MATHEMATICS | Poincare duality space | MATHEMATICS, APPLIED | group action

Mathematical manifolds | Mathematical theorems | Algebra | Logical proofs | Mathematical duality | Polynomials | Mathematical congruence | Coefficients | College mathematics | Induction assumption | Group action | Poincaré duality space | Betti number | MATHEMATICS | Poincare duality space | MATHEMATICS, APPLIED | group action

Journal Article

Topology and its Applications, ISSN 0166-8641, 2004, Volume 142, Issue 1, pp. 1 - 12

For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost...

Isometry | Hausdorff metric | Almost periodic | MATHEMATICS | MATHEMATICS, APPLIED | almost periodic | isometry

Isometry | Hausdorff metric | Almost periodic | MATHEMATICS | MATHEMATICS, APPLIED | almost periodic | isometry

Journal Article

数理解析研究所講究録, ISSN 1880-2818, 04/2015, Volume 1938, pp. 10 - 14

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 10/2016, Volume 11, Issue 5, pp. 1189 - 1206

We discuss the topology and geometry of closed Alexandrov spaces of dimension three.

53C23 | 57S10 | 3-manifold | Mathematics, general | Mathematics | group action | Alexandrov space | METRIC-MEASURE-SPACES | INVOLUTIONS | CLASSIFICATION | MATHEMATICS | ISOMETRY GROUPS | CURVATURE | 3-MANIFOLDS | 3-SPHERE | MANIFOLDS | FIXED-POINTS | GEOMETRY | Studies | Topological manifolds | Mathematical analysis | Topology

53C23 | 57S10 | 3-manifold | Mathematics, general | Mathematics | group action | Alexandrov space | METRIC-MEASURE-SPACES | INVOLUTIONS | CLASSIFICATION | MATHEMATICS | ISOMETRY GROUPS | CURVATURE | 3-MANIFOLDS | 3-SPHERE | MANIFOLDS | FIXED-POINTS | GEOMETRY | Studies | Topological manifolds | Mathematical analysis | Topology

Journal Article

Dynamical Systems, ISSN 1468-9367, 10/2014, Volume 29, Issue 4, pp. 502 - 516

Let G be a positively equicontinuous flow of homeomorphisms of a locally compact metric space E. We show how the dynamics of such a flow are rich. We study...

positively equicontinuous flows of homeomorphisms | Lie group | limit set | periodic | regularly almost periodic | MATHEMATICS, APPLIED | 54H20 | 37B05 | MECHANICS | 57S05 | 37B20 | 57S10 | ALMOST-PERIODIC HOMEOMORPHISMS | Orbits | Metric space | Dynamics | Dynamical systems

positively equicontinuous flows of homeomorphisms | Lie group | limit set | periodic | regularly almost periodic | MATHEMATICS, APPLIED | 54H20 | 37B05 | MECHANICS | 57S05 | 37B20 | 57S10 | ALMOST-PERIODIC HOMEOMORPHISMS | Orbits | Metric space | Dynamics | Dynamical systems

Journal Article

03/2013

We present a new approach to equivariant version of the topological complexity, called a symmetric topological complexity. It seems that the presented approach...

Journal Article

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