FINITE COMPLEXES WHOSE SELF-HOMOTOPY EQUIVALENCES FORM CYCLIC GROUPS

Finite groups all of whose proper centralizers are cyclic

‎A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic‎. ‎In this article we determine all finite $CC$-groups.

Reducibility of Self-homotopy Equivalences

We describe a new general method for the computation of the group Aut(X) of self-homotopy equivalences of a space. It is based on the decomposition of Aut(X) induced by a factorization of X into a product of simpler spaces. Normally, such decompositions require assumptions (’induced equivalence property’, ’diagonalizability’), which are strongly restrictive and hard to check. In this paper we d...

Geometric Chain Homotopy Equivalences between Novikov Complexes

We give a detailed account of the Novikov complex corresponding to a closed 1-form ω on a closed connected smooth manifold M . Furthermore we deduce the simple chain homotopy type of this complex using various geometrically defined chain homotopy equivalences and show how they are related to another.

Combinatorial group theory and the homotopy groups of finite complexes

A description of homotopy groups of the 2-dimensional sphere in terms of combinatorial group theory was discovered by the second author in 1994 and given in his thesis [25], with a published version in [27]. In this article we give a combinatorial description of the homotopy groups of k-dimensional spheres with k ≥ 3. The description is given by identifying the homotopy groups as the center of ...

Self-Homotopy Equivalences of Product Spaces