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Spaces which Invert Weak Homotopy Equivalences
(Cambridge University Press, 2019-05)
It is well known that if X is a CW-complex, then for every weak homotopy equivalence f : A → B, the map f: [X, A] → [X, B] induced in homotopy classes is a bijection. In fact, up to homotopy equivalence, only CW-complexes ...
Homotopy type of gauge groups of quaternionic line bundles over spheres
(ELSEVIER SCIENCE BV, 2009)
Let P be a principal S(3)-bundle over a sphere S(n), with n >= 4. Let G(p) be the gauge group of P. The homotopy type of G(p) when n - 4 was studied by A. Kono in [A. Kono, A note on the homotopy type of certain gauge ...
Star clusters in independence complexes of graphs
(Academic Press Inc Elsevier Science, 2013-03)
We introduce the notion of star cluster of a simplex in a simplicial complex. This concept provides a general tool to study the topology of independence complexes of graphs. We use star clusters to answer a question arisen ...
The fixed point property in every weak homotopy type
(Johns Hopkins Univ Press, 2016-01)
We prove that for any connected compact CW-complex K there exists aspace X weak homotopy equivalent to K which has the fixed point property, that is,every continuous map X -> X has a fixed point. The result is known to be ...
Some equivalences between homotopy and derived categories
(Universidad de AllahabadÁlgebra Teoría de Números y Aplicaciones: ERMÁlgebra U de AAllahabad, India, 2022)
The Borsuk-Ulam theorem for homotopy spherical space forms
(BIRKHAUSER VERLAG AG, 2011)
In this work, we show for which odd-dimensional homotopy spherical space forms the Borsuk-Ulam theorem holds. These spaces are the quotient of a homotopy odd-dimensional sphere by a free action of a finite group. Also, the ...
THE HOMOTOPY TYPE OF INVARIANT CONTROL SET
(Universidad Católica del Norte, Departamento de Matemáticas, 2002)
Strong Homotopy Types, Nerves and Collapses
(Springer, 2012-03)
We introduce the theory of strong homotopy types of simplicial complexes. Similarly to classical simple homotopy theory, the strong homotopy types can be described by elementary moves. An elementary move in this setting ...
Classical Morse Theory Revisited - I Backward Lambda-lemma And Homotopy Type
(Juliusz Schauder CTR Nonlinear StudiesTorun, 2016)
Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))
(ELSEVIER SCIENCE BV, 2009)
Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of ...