Mathematika, ISSN 0025-5793, 01/2020, Volume 66, Issue 1, pp. 79 - 102

Thickenings of a metric space capture local geometric properties of the space. Here, we exhibit applications of lower bounding the topology of thickenings of...

05E45 (primary) | 52B15 | 54E35 | 55P10 | 55U10 (secondary)

05E45 (primary) | 52B15 | 54E35 | 55P10 | 55U10 (secondary)

Journal Article

Selecta Mathematica, ISSN 1022-1824, 3/2019, Volume 25, Issue 1, pp. 1 - 11

The amplituhedra arise as images of the totally nonnegative Grassmannians by projections that are induced by linear maps. They were introduced in Physics by...

Mathematics, general | 15B48 | Mathematics | 55P10 | 14M15 | 55Rxx | MATHEMATICS | MATHEMATICS, APPLIED

Mathematics, general | 15B48 | Mathematics | 55P10 | 14M15 | 55Rxx | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Forum Mathematicum, ISSN 0933-7741, 03/2017, Volume 29, Issue 2, pp. 465 - 488

We give a self-contained and purely combinatorial proof of the well-known fact that the cohomology of the braces operad is the operad governing Gerstenhaber...

the Deligne conjecture on Hochschild cochains | 55P10 | 18D50 | homotopy algebras | 18G55 | Algebraic operads | MATHEMATICS | FORMALITY | MATHEMATICS, APPLIED | CACTI

the Deligne conjecture on Hochschild cochains | 55P10 | 18D50 | homotopy algebras | 18G55 | Algebraic operads | MATHEMATICS | FORMALITY | MATHEMATICS, APPLIED | CACTI

Journal Article

Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 10/2017, Volume 23, Issue 2, pp. 847 - 851

Let Aut(p) denote the space of all self-fibre homotopy equivalences of a principal G-bundle $$p: E\rightarrow X$$ p : E → X of simply connected CW complexes...

Fibre homotopy equivalence | Sullivan minimal model | Derivation | 55P62 | Mathematics, general | Mathematics | Samelson–Lie algebra | 55P10

Fibre homotopy equivalence | Sullivan minimal model | Derivation | 55P62 | Mathematics, general | Mathematics | Samelson–Lie algebra | 55P10

Journal Article

Georgian Mathematical Journal, ISSN 1072-947X, 2018

Abstract We address the (pointed) homotopy of crossed module morphisms in modified categories of interest that unify the notions of groups and various...

Crossed module | simplicial object | homotopy | modified categories of interest

Crossed module | simplicial object | homotopy | modified categories of interest

Journal Article

Topological Algebra and its Applications, ISSN 2299-3231, 04/2017, Volume 5, Issue 1, pp. 13 - 18

Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃ℜ̅ by x̃ ̃ℜ̅y if the closure of the R-trajectory of...

orbit class space | 55P15 | 18B35 | orbit space | leaf class space | 54B15 | 54F65 | Homotopy | leaf space | 55P10

orbit class space | 55P15 | 18B35 | orbit space | leaf class space | 54B15 | 54F65 | Homotopy | leaf space | 55P10

Journal Article

Topology and its Applications, ISSN 0166-8641, 05/2015, Volume 185-186, pp. 93 - 123

This paper shows that a functorial version of the “higher diagonal” of a space used to compute Steenrod squares actually contains far more topological...

Homotopy theory | Operads | Completions | Coalgebras | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Algebraic Topology

Homotopy theory | Operads | Completions | Coalgebras | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Algebraic Topology

Journal Article

Geometry and Topology, ISSN 1465-3060, 2015, Volume 19, Issue 3, pp. 1383 - 1407

Let G be a complex reductive linear algebraic group and let K subset of G be a maximal compact subgroup. Given a nilpotent group Gamma generated by r elements,...

ALGEBRAIC-GROUPS | MATHEMATICS | TUPLES | SPACES | CHARACTER VARIETIES

ALGEBRAIC-GROUPS | MATHEMATICS | TUPLES | SPACES | CHARACTER VARIETIES

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2011, Volume 269, Issue 3, pp. 1189 - 1199

For $${M_r := \sharp_r(S^p \times S^p),\,p=3, 7}$$ , we calculate $${\pi_0{\rm Diff}(M_r)/\Theta_{2p+1}}$$ and $${\mathcal{E}(M_r)}$$ , respectively the group...

Self-homotopy equivalences | 57R52 | Mathematics, general | Mathematics | Mapping class groups | 55P10

Self-homotopy equivalences | 57R52 | Mathematics, general | Mathematics | Mapping class groups | 55P10

Journal Article

Mathematische annalen, ISSN 0025-5831, 2012, Volume 356, Issue 1, pp. 23 - 43

Let $$M$$ be a Riemannian manifold and let $$\varOmega $$ be a bounded open subset of $$M$$ . It is well known that significant information about the geometry...

Mathematics, general | 35A21 | Mathematics | 26B25 | 55P10 | 49J52 | MATHEMATICS | HAMILTON-JACOBI EQUATIONS | Optimization and Control | Differential Geometry | Analysis of PDEs

Mathematics, general | 35A21 | Mathematics | 26B25 | 55P10 | 49J52 | MATHEMATICS | HAMILTON-JACOBI EQUATIONS | Optimization and Control | Differential Geometry | Analysis of PDEs

Journal Article

Mathematische Annalen, ISSN 0025-5831, 10/2011, Volume 351, Issue 2, pp. 281 - 303

Topological free involutions on S 1 × S n are classified up to conjugation. We prove that this is the same as classifying quotient manifolds up to...

57S25 | Mathematics, general | Mathematics | 55P10 | 57R67

57S25 | Mathematics, general | Mathematics | 55P10 | 57R67

Journal Article

Journal of Homotopy and Related Structures, ISSN 2193-8407, 4/2014, Volume 9, Issue 1, pp. 67 - 84

We compute the homology of the spaces of directed paths on a certain class of cubical subcomplexes of the directed Euclidean space $$\mathbb{R }^n$$ R n by a...

Cubical complex | Algebraic Topology | Directed paths | Homology | Mathematics | Cohomology | 55P10 | 55P15 | 55U10 | Algebra | Functional Analysis | Number Theory | Path space | 68Q85 | MATHEMATICS

Cubical complex | Algebraic Topology | Directed paths | Homology | Mathematics | Cohomology | 55P10 | 55P15 | 55U10 | Algebra | Functional Analysis | Number Theory | Path space | 68Q85 | MATHEMATICS

Journal Article

Afrika Matematika, ISSN 1012-9405, 9/2016, Volume 27, Issue 5, pp. 851 - 864

Our goal in this paper is to give a full classification of the rational homotopy type of any elliptic and simply connected space when the sum of its Betti...

Rational homotopy theory | Rational homotopy type | Mathematics | History of Mathematical Sciences | 55Q52 | Primary 55P62 | Sullivan models | 55P15 | 55Q05 | Secondary 55P10 | Mathematics, general | Mathematics Education | Applications of Mathematics | Elliptic spaces

Rational homotopy theory | Rational homotopy type | Mathematics | History of Mathematical Sciences | 55Q52 | Primary 55P62 | Sullivan models | 55P15 | 55Q05 | Secondary 55P10 | Mathematics, general | Mathematics Education | Applications of Mathematics | Elliptic spaces

Journal Article

Computational and Applied Mathematics, ISSN 0101-8205, 3/2017, Volume 36, Issue 1, pp. 127 - 144

To digitize subspaces of the Euclidean $$n$$ n D space, the present paper uses the Khalimsky (for short $$K$$ K -, if there is no danger of ambiguity)...

54C10 | 68U10 | Computational Mathematics and Numerical Analysis | K$$ K -localized neighborhood | Digital topology | A$$ A -isomorphism | Mathematics | 54C05 | Khalimsky $$n$$ n D space | 55P10 | 68U05 | Mathematical morphology | 54C08 | 55P15 | Mathematical Applications in Computer Science | A$$ A -map | Digitization | Applications of Mathematics | Khalimsky adjacency | LA$$ L A -isomorphism | Mathematical Applications in the Physical Sciences | LA$$ L A -map | Local rule

54C10 | 68U10 | Computational Mathematics and Numerical Analysis | K$$ K -localized neighborhood | Digital topology | A$$ A -isomorphism | Mathematics | 54C05 | Khalimsky $$n$$ n D space | 55P10 | 68U05 | Mathematical morphology | 54C08 | 55P15 | Mathematical Applications in Computer Science | A$$ A -map | Digitization | Applications of Mathematics | Khalimsky adjacency | LA$$ L A -isomorphism | Mathematical Applications in the Physical Sciences | LA$$ L A -map | Local rule

Journal Article

Central European Journal of Mathematics, ISSN 1895-1074, 9/2014, Volume 12, Issue 9, pp. 1330 - 1336

We prove that for n > 1 the space of proper maps P 0(n, k) and the space of local maps F 0(n, k) are not homotopy equivalent.

Geometry | Algebra | Local map | Topological Groups, Lie Groups | 54C35 | Proper map | Homotopy equivalence | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Number Theory | 55P10 | MATHEMATICS

Geometry | Algebra | Local map | Topological Groups, Lie Groups | 54C35 | Proper map | Homotopy equivalence | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Number Theory | 55P10 | MATHEMATICS

Journal Article

Journal of Homotopy and Related Structures, ISSN 2193-8407, 9/2015, Volume 10, Issue 3, pp. 549 - 564

Let $$R \subseteq {\mathbb Q}$$ R ⊆ Q be a ring with least non-invertible prime $$p$$ p . Let $$X = X^{n} \cup _{\alpha } (\bigcup _{j \in J} e^{q})$$ X = X n...

R$$ R -local homotopy theory Moore space | Anick model | Algebra | Functional Analysis | Algebraic Topology | Quillen model | Nilpotent group | Homotopy self-equivalences | Mathematics | Number Theory | 55P10

R$$ R -local homotopy theory Moore space | Anick model | Algebra | Functional Analysis | Algebraic Topology | Quillen model | Nilpotent group | Homotopy self-equivalences | Mathematics | Number Theory | 55P10

Journal Article

Journal of Homotopy and Related Structures, ISSN 2193-8407, 9/2017, Volume 12, Issue 3, pp. 691 - 706

Let $$\mathcal {E}(X)$$ E ( X ) be the group of homotopy classes of self homotopy equivalences for a connected CW complex X. We consider two classes of maps,...

mathcal {E}$$ E -Map | Algebraic Topology | Rationally $$\mathcal {E}$$ E -equivalent | 55P62 | Mathematics | 55P10 | Algebra | Rational co- $$\mathcal {E}$$ E -map | Functional Analysis | Sullivan (minimal) model | Rational homotopy | Co- $$\mathcal {E}$$ E -map | Rational $$\mathcal {E}$$ E -map | Number Theory | Self homotopy equivalence | E-Map | Rational co-E-map | Rationally E-equivalent | Co-E-map | Rational E-map | MATHEMATICS | Co-epsilon-map | epsilon-Map | Rationally epsilon-equivalent | Rational epsilon-map | Rational co-epsilon-map

mathcal {E}$$ E -Map | Algebraic Topology | Rationally $$\mathcal {E}$$ E -equivalent | 55P62 | Mathematics | 55P10 | Algebra | Rational co- $$\mathcal {E}$$ E -map | Functional Analysis | Sullivan (minimal) model | Rational homotopy | Co- $$\mathcal {E}$$ E -map | Rational $$\mathcal {E}$$ E -map | Number Theory | Self homotopy equivalence | E-Map | Rational co-E-map | Rationally E-equivalent | Co-E-map | Rational E-map | MATHEMATICS | Co-epsilon-map | epsilon-Map | Rationally epsilon-equivalent | Rational epsilon-map | Rational co-epsilon-map

Journal Article

数学物理学报：B辑英文版, ISSN 0252-9602, 2014, Volume 34, Issue 4, pp. 1193 - 1211

In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also...

代数 | c循环 | CO-H-空间 | co-H-spaces | algebraic loops | inverses | comultiplications | 55P10 | 55Q20 | inversivity | Hopf-Hilton invariants | power-associativity | 55P45 | 20M32 | basic (Whitehead) product | Moufang property | Inverses | Basic (Whitehead) product | Inversivity | Algebraic loops | Power-associativity | Comultiplications | Co-H-spaces | MATHEMATICS | SUSPENSION | WEDGE | Construction | Algebra | Wedges | Mathematical analysis

代数 | c循环 | CO-H-空间 | co-H-spaces | algebraic loops | inverses | comultiplications | 55P10 | 55Q20 | inversivity | Hopf-Hilton invariants | power-associativity | 55P45 | 20M32 | basic (Whitehead) product | Moufang property | Inverses | Basic (Whitehead) product | Inversivity | Algebraic loops | Power-associativity | Comultiplications | Co-H-spaces | MATHEMATICS | SUSPENSION | WEDGE | Construction | Algebra | Wedges | Mathematical analysis

Journal Article

Combinatorica (Budapest. 1981), ISSN 0209-9683, 2007, Volume 27, Issue 6, pp. 669 - 682

In [14] Matoušek and Ziegler compared various topological lower bounds for the chromatic number. They proved that Lovász’s original bound [9] can be restated...

05C10 | Mathematics, general | Mathematics | 55P10 | Combinatorics | 05C15 | MATHEMATICS | KNESER CONJECTURE | MAPS | GRAPHS

05C10 | Mathematics, general | Mathematics | 55P10 | Combinatorics | 05C15 | MATHEMATICS | KNESER CONJECTURE | MAPS | GRAPHS

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 6/2008, Volume 259, Issue 2, pp. 311 - 319

Let G be a compact subgroup of an orthogonal group and X an affine, real, semialgebraic Nash variety. A principal Nash G-bundle over X is said to be strongly...

55R35 | 55R25 | 55R10 | Mathematics, general | Mathematics | 55P10 | 32C05 | MATHEMATICS

55R35 | 55R25 | 55R10 | Mathematics, general | Mathematics | 55P10 | 32C05 | MATHEMATICS

Journal Article

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