The problem of equivariant rigidity is the Γ-homeomorphism classification of Γ-actions on manifolds with compact quotient and with contractible fixed sets for all finite subgroups of Γ. In other words, this is the classification of cocompact EfinΓ-manifolds. We use surgery theory, algebraic K-theory, and the Farrell–Jones Conjecture to give this classification for a family of groups which satis...

The main concept of this classification is that graphs belonging to the same equivalence class have similar topological properties. Graphs are called homotopy equivalent if one of them can be converted to the other one by contractible transformations. A basic representative and complexity of a homotopy equivalence class are defined and investigated. Finding a basic representative within a homot...

a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...

In this paper we defined the concept of module amenability of Banach algebras and module connes amenability of module dual Banach algebras.Also we assert the concept of module Arens regularity that is different with [1] and investigate the relation between module amenability of Banach algebras and connes module amenability of module second dual Banach algebras.In the following we studythe...

A structural description is given of the separable C algebras that are contractible in KK theory or E theory Subsequently it is shown that two separable C algebras A and B are KK equivalent if and only if there is a bundle of separable C algebras over which is piecewise trivial with no more than six points of non triviality such that the kernel of each ber map is KK contractible all ber maps ar...

An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. In this paper, we prove that a (K1 + C4)-free minimally k-connected graph has a k-contractible edge, if incident to each vertex of degree k, there is an edge which is not contained in a triangle. This implies two previous results, one due to Thomassen and the other due to K...

A polynomial time isomorphism test for graphs called k-contractible graphs for fixed k is included. The class of k-contractible graphs includes the graphs of bounded valence and the graphs of bounded genus. The algorithm several new ideas including: (1) It removes portions of the graph and replaces them with groups which are used to keep track of the symmetries of these portions. (2) It maintai...

In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible. Our method is to ex...

The state spaces of machines admit the structure of time. A homotopy theory respecting this additional structure can detect machine behavior unseen by classical homotopy theory. In an attempt to bootstrap classical tools into the world of abstract spacetime, we identify criteria for classically homotopic, monotone maps of pospaces to future homotope, or homotope along homotopies monotone in bot...

Associated to any Coxeter system (W,S), there is a labeled simplicial complex L and a contractible CW-complex ΣL (the Davis complex) on which W acts properly and cocompactly. ΣL admits a cellulation under which the nerve of each vertex is L. It follows that if L is a triangulation of S , then ΣL is a contractible n-manifold. We prove that a special case of the Singer conjecture for ΣL (on the v...