Related papers: Fixed Point Sets and the Fundamental Group II: Eul…

Generating functions for the number of commuting m-tuples in the symmetric groups are obtained. We define a natural sequence of ``orbifold Euler characteristics'' for a finite group G acting on a manifold X. Our definition generalizes the…

The special linear group G=SL_n(Z[x1,...,xk]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, p be any real number in (1,\infty). The main result is the following: any finite index subgroup of G has the…

For all $k \ge 2$, we show that there exists a group $G$ and a non-free stably free $\mathbb{Z} G$-module of rank $k$. We use this to show that, for all $k \ge 2$, there exist homotopically distinct finite $2$-complexes with fundamental…

We consider the group $\mathfrak{X}(G)$ obtained from $G\ast G$ by forcing each element $g$ in the first free factor to commute with the copy of $g$ in the second free factor. Deceptively complicated finitely presented groups arise from…

The Brouwer fixed point theorem states that the disk $D^n$ has the fixed point property. More generally, by the Lefschetz fixed point theorem any compact ANR with trivial rational homology has the fixed point property. In this note we prove…

Let $G$ be a finite group and $N\unlhd G$. In this note, we construct a class poset of $G$ for some cyclic subgroup $C$ of $G$. And we find a relation between $m_{G,N}$ and the Euler characteristic of some nerve spaces of these posets(see…

Let G be a locally compact group, let X be a universal proper G-space, and let Z be a G-equivariant compactification of X that is H-equivariantly contractible for each compact subgroup H of G. Let W be the resulting boundary. Assuming the…

Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is the fixed point subspace of an element of G. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then…

We prove that the minimal Euler characteristic of a closed symplectic four-manifold with given fundamental group is often much larger than the minimal Euler characteristic of almost complex closed four-manifolds with the same fundamental…

Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact sigma-compact…

The notion of the truncated Euler characteristic for Iwasawa modules is an extension of the notion of the usual Euler characteristic to the case when the homology groups are not finite. This article explores congruence relations between the…

In this paper we consider the finite groups that act fiber- and orientation-preservingly on closed, compact, and orientable Seifert manifolds that fiber over an orientable base space. We establish a method of constructing such group actions…

We prove that if $F$ is a finitely generated abelian group of orientation preserving $C^1$ diffeomorphisms of $R^2$ which leaves invariant a compact set then there is a common fixed point for all elements of $F.$ We also show that if $F$ is…

Let p be a prime number, G a finite group, and A a finite group acting on G. The Brown poset of nonidentity p-subgroups of G is then an A-poset. We investigate the equivariant subposet and the equivariant Euler characteristics and establish…

We first obtain finiteness properties for the collection of closed normal subgroups of a compactly generated locally compact group. Via these properties, every compactly generated locally compact group admits an essentially chief series -…

By a result of Klyachko the Euler characteristic of moduli spaces of stable bundles of rank two on the projective plane is determined. Using similar methods we extend this result to bundles of rank three. The fixed point components…

We show that, if $w_1, \ldots , w_6$ are words which are not an identity of any (non-abelian) finite simple group, then $w_1(G)w_2(G) \cdots w_6(G) = G$ for all (non-abelian) finite simple groups $G$. In particular, for every word $w$,…

We show that certain representations over fields with positive characteristic of groups having CAT(0) fixed point property ${\rm F}\mathcal{B}_{\widetilde{A}_n}$ have finite image. In particular, we obtain rigidity results for…

We show that every real analytic action of a connected supersoluble Lie group on a compact surface with nonzero Euler characteristic has a fixed point. This implies that E. Lima's fixed point free $C^{\infty}$ action on $S^2$ of the affine…

Let G be a classical group over an algebraically closed field of characteristic 2 and let C be an elliptic conjugacy class in the Weyl group. In a previous paper the first named author associated to C a unipotent conjugacy class \Phi(C) in…