Related papers: Sigma 1 of PL-homeomorphism groups

In this paper, we define (reduced) homeology groups and (reduced) cohomeology groups on finite simpicial complexes and prove that these groups are PL homeomorphsm invariants of polyhedra, while they are not homotopy invariants. So these…

In this paper we study finite groups which have Cayley isomorphism property with respect to Cayley maps, CIM-groups for a brief. We show that the structure of the CIM-groups is very restricted. It is described in Theorem~\ref{111015a} where…

For locally finite infinite graphs the notion of Hamilton cycles can be extended to Hamilton circles, homeomorphic images of $S^1$ in the Freudenthal compactification. In this paper we prove of a sufficient condition for the existence of…

In this article we describe relations of the topology of closed 1-forms to the group theoretic invariants of Bieri-Neumann-Strebel-Renz. Starting with a survey, we extend these Sigma invariants to finite CW- complexes and show that many…

In this article, we describe all the group morphisms from the group of compactly-supported homeomorphisms isotopic to the identity of a manifold to the group of homeomorphisms of the real line or of the circle.

We show that certain groups of piecewise linear homeomorphims of the interval are invariably generated.

This survey purports to be an elementary introduction to compactly presented groups, which are the analogue of finitely presented groups in the broader realm of locally compact groups. In particular, compact presentation is interpreted as a…

For locally finite infinite graphs the notion of Hamilton cycles can be extended to Hamilton circles, homeomorphic images of $S^1$ in the Freudenthal compactification. In this paper we extend some well-known theorems of the Hamiltonicity of…

In a previous paper the author constructed biinvariant measures (possibly having values in a line bundle) for a loop group LK (with compact simply connected K) acting on the formal completion of its complexification LG. One motivation for…

In this paper we develop the homological version of $\Sigma$-theory for locally compact Hausdorff groups, leaving the homotopical version for another paper. Both versions are connected by a Hurewicz-like theorem. They can be thought of as…

This is a survey on left invariant semi-Riemannian metrics on compact Lie groups.

In this note we study topological invariants of the spaces of homomorphisms Hom(\pi,G), where \pi\ is a finitely generated abelian group and G is a compact Lie group arising as an arbitrary finite product of the classical groups SU(r), U(q)…

In this paper, we define a new bigraded L-homology on finite simplicial complexes and prove that L-homology is a homeomorphism invariant of polyhedra.

In this paper, we construct a family of quasi-strongly regular Cayley graphs $\Gamma_H(G)$ which is defined on a finite group $G$ with respect to a subgroup $H$ of $G$. We also compute its full automorphism group and characterize various…

We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications,…

Let $G$ be a finite group. For each $m>1$ we define the symmetric canonical subset $S=S(m)$ of the Cartesian power $G^m$ and we consider the family of Cayley graphs $\mathscr{G}_m(G)=Cay(G^m,S)$. We describe properties of these graphs and…

Thompson's group F is the group of all increasing dyadic piecewise linear homeomorphisms of the closed unit interval. We compute Sigma^m(F) and Sigma^m(F;Z), the homotopical and homological Bieri-Neumann-Strebel-Renz invariants of F, and we…

In a series of papers the authors associated to an $L^2$-acyclic group $\Gamma$ an invariant $\mathcal{P}(\Gamma)$ that is a formal difference of polytopes in the vector space $H_1(\Gamma;\Bbb{R})$. This invariant is in particular defined…

In this work, we prove that, under a topological condition, the cohomology associated with left-invariant elliptic structures on compact semisimple Lie groups can be computed using only left-invariant forms. This reduces the analytical…

Inspired by the work of Chevalley and Eilenberg on the de Rham cohomology on compact Lie groups, we prove that, under certain algebraic and topological conditions, the cohomology associated to left-invariant elliptic, and even hypocomplex,…