Displaying similar documents to “Linking and coincidence invariants”

Some homotopy theoretical questions arising in Nielsen coincidence theory

Ulrich Koschorke (2009)

Banach Center Publications

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Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We recall some recent results and ask a few questions which seem to be important for a more comprehensive understanding.

Embedding proper homotopy types

M. Cárdenas, T. Fernández, F. F. Lasheras, A. Quintero (2003)

Colloquium Mathematicae

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We show that the proper homotopy type of any properly c-connected locally finite n-dimensional CW-complex is represented by a closed polyhedron in ℝ 2 n - c (Theorem I). The case n - c ≥ 3 is a special case of a general proper homotopy embedding theorem (Theorem II). For n - c ≤ 2 we need some basic properties of “proper” algebraic topology which are summarized in Appendices A and B. The results of this paper are the proper analogues of classical results by Stallings [17] and Wall [20] for finite...

On the homotopy type of Diff ( M n ) and connected problems

Dan Burghelea (1973)

Annales de l'institut Fourier

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This paper reports on some results concerning: a) The homotopy type of the group of diffeomorphisms Diff ( M n ) of a differentiable compact manifold M n (with C ∞ -topology). b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo M n (with C o -topology). As a biproduct, one gets new facts about the homotopy groups of Diff ( D n , ∂ D n ) , Top n , Top n / O n and about the number of connected components of the space of topological and combinatorial pseudoisotopies. ...

Homotopy over B and under A

K. A. Hardie, K. H. Kamps (1987)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Some results on homotopy theory of modules

Zheng-Xu He (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Seguendo le idee presentate nei lavori [1] e [2] si studiano le proprietà dei gruppi di i -omotopia per moduli ed omomorfismi di moduli.

Link homotopy invariants of graphs in R.

Kouki Taniyama (1994)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we define a link homotopy invariant of spatial graphs based on the second degree coefficient of the Conway polynomial of a knot.

G-ANR's with homotopy trivial fixed point sets

Sergey A. Antonyan (2007)

Fundamenta Mathematicae

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Let G be a compact group and X a G-ANR. Then X is a G-AR iff the H-fixed point set X H is homotopy trivial for each closed subgroup H ⊂ G.

Minimal component numbers of fixed point sets

Xuezhi Zhao (2003)

Fundamenta Mathematicae

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Let f: (X,A) → (X,A) be a relative map of a pair of compact polyhedra. We introduce a new relative homotopy invariant N C ( f ; X , A ) , which is a lower bound for the component numbers of fixed point sets of the self-maps in the relative homotopy class of f. Some properties of N C ( f ; X , A ) are given, which are very similar to those of the relative Nielsen number N(f;X,A).

G-functors, G-posets and homotopy decompositions of G-spaces

Stefan Jackowski, Jolanta Słomińska (2001)

Fundamenta Mathematicae

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We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map h o c o l i m d G / d ( - ) → | W | which is a (non-equivariant) homotopy equivalence, hence h o c o l i m d E G × G F d → E G × G | W | is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy...