Related papers: Z_2 actions on complexes with three non-trivial ce…

Let $X$ be a finitistic space with its rational cohomology isomorphic to that of the wedge sum $P^2(n)\vee S^{3n} $ or $S^{n} \vee S^{2n}\vee S^{3n}$. We study continuous $\mathbb{S}^1$ actions on $X$ and determine the possible fixed point…

We study the symplectic action of the group (Z/2Z)^2 on a K3 surface X: we describe its action on H^2(X,Z) and the maps induced in cohomology by the rational quotient maps; we give a lattice-theoretic characterization of the resolution of…

Let X be a finitistic space with non-trivial cohomology groups H^in(X;Z)=Z with generators v_i, where i = 0, 1, 2, 3. We say that X has cohomology type (a, b) if v_1^2 = av_2 and v_1v_2 = bv_3 . In this note, we determine the mod 2…

We prove that for every compactum X with dim_Z X <= n >= 2 there is a cell-like resolution r: Z --> X from a compactum Z onto X such that dim Z <= n and for every integer k and every abelian group G such that dim_G X <= k >= 2 we have dim_G…

If $X$ is a connected complex manifold with $d_X = 2$ that admits the holomorphic and transitive action of a (connected) Lie group $G$, then the action extends to an action of the complexification $\hat{G}$ of $G$ on $X$ except when either…

We study simplicial action of groups on one vertex Kan complexes. We show that every semi-direct product of the fundamental group of an one vertex Kan complex with a finite group can be simplicially realized. We also calculate the…

Let $X$ be a finite CW-complex having mod $p$ cohomology isomorphic to a wedge of three spheres $\mathbb{S}^n\vee \mathbb{S}^m \vee \mathbb{S}^l,~ 1\leq n \leq m \leq l$. The aim of this paper is to determine the fixed point sets of actions…

It is proved that if S^6 possesses an integrable complex structure, then there exists a 1-dimensional family of pairwise different exotic complex structures on P_3(C). This follows immediately from the main result of the paper: S^6 is not…

In this paper we show that the cohomology of a connected CW complex is periodic if and only if it is the base space of an orientable spherical fibration with total space that is homotopically finite dimensional. As applications we…

Let $V$ be an elementary abelian $2$-group and $X$ be a finite $V$-CW-complex. In this memoir we study two cochain complexes of modules over the mod2 Steenrod algebra $\mathrm{A}$, equipped with an action of $\mathrm{H}^{*}V$, the mod2…

Let G be either a finite cyclic group of prime order or S^1. We find new relations between cohomology of a manifold (or a Poincare duality space) M with a G-action on it and cohomology of the fixed point set, M^G. Our main tool is the…

Let the circle act in a Hamiltonian fashion on a compact symplectic manifold $(M, \omega)$ of dimension $2n$. Then the $S^1$-action has at least $n+1$ fixed points. We study the case when the fixed point set consists of precisely $n+1$…

An algebraic $Z^{d}$-action is an action of $Z^{d}$ on a compact abelian group $X$ by automorphisms of $X$. We prove that for $d \ge 8$, there exist mixing zero entropy algebraic $Z^{d}$-actions which do not exhibit isomorphism rigidity…

Let G be a finite group acting freely on a finitistic space X having cohomology type (0, b) (for example, S^n x S^{2n} is a space of type (0, 1) and the one-point union S^n V S^{2n} V S^{3n} is a space of type (0, 0)). It is known that a…

In this paper, we study finite symplectic actions on K3 surfaces X, i.e. actions of finite groups G on X which act on H^{2,0}(X) trivially. We show that the action on the K3 lattice H^2(X,Z) induced by a symplectic action of G on X depends…

Let the compact torus $T^{n-1}$ act on a smooth compact manifold $X^{2n}$ effectively with nonempty finite set of fixed points. We pose the question: what can be said about the orbit space $X^{2n}/T^{n-1}$ if the action is cohomologically…

We compute the cohomology of the unordered configuration spaces of the sphere $S^2$ with integral and with $\mathbb{Z}/p \mathbb{Z}$-coefficients using a cell complex by Fuks, Vainshtein and Napolitano.

Any continuous action of SL(n,Z), where n > 2, on a r-dimensional mod 2 homology sphere factors through a finite group action if r < n - 1. In particular, any continuous action of SL(n+2,Z) on the n-dimensional sphere factors through a…

Let $G$ be a group acting freely, properly discontinuously and cellularly on a finite dimensional $C$W-complex $\Sigma(2n)$ which has the homotopy type of the $2n$- sphere $\mathbb{S}^{2n}$. Then, this action induces an action of the group…

Let $\Gamma$ = SL 3 (Z[ 1 2 , i]), let X be any mod-2 acyclic $\Gamma$-CW complex on which $\Gamma$ acts with finite stabilizers and let Xs be the 2-singular locus of X. We calculate the mod-2 cohomology of the Borel constructon of Xs with…