Related papers: Borsuk-Ulam type theorems for manifolds

Let M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related…

In this paper, we show Langton's type theorem on separatedness and properness of moduli functor of torsion free semistable sheaves on algebraic orbifolds over an algebraically closed field k

In this paper, we introduce a category of graded commutative rings with certain algebraic morphisms, to investigate the cobordism category of plumbed 3-manifolds. In particular, we define a non-associative distributive algebra that gives…

A generalization of the classical Leray-Schauder fixed point theorem, based on the in finite- dimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on…

Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…

This paper is a survey on the Lickorish type construction of some kind of closed manifolds over simple convex polytopes. Inspired by Lickorish's theorem, we propose a method to describe certain families of manifolds over simple convex…

In view of the Segal construction each category with a coherent operation gives rise to a cohomology theory. Similarly each open stable differential relation $R$ imposed on smooth maps of manifolds determines cohomology theories $k^*$ and…

Let $M$ be a locally symmetric irreducible closed manifold of dimension $\ge 3$. A result of Borel [Bo] combined with Mostow rigidity imply that there exists a finite group $G = G(M)$ such that any finite subgroup of $\text{Homeo}^+(M)$ is…

We show, up to h-cobordism, that the existence and uniqueness of connected sum decompositions of oriented 4-dimensional manifolds is an invariant of homotopy equivalence, assuming that the fundamental group of each summand is "good" in the…

We give complete geometric invariants of cobordisms of fold maps with oriented singular set and cobordisms of even codimensional fold maps. These invariants are given in terms of cobordisms of stably framed manifolds and cobordisms of…

We introduce a torsor-theoretic obstruction to equivariant unirationality and show that it is also sufficient for actions of finite groups on toric varieties arising from automorphisms of the torus.

We present two versions of the Egorov theorem for orbifolds. The first one is a straightforward extension of the classical theorem for smooth manifolds. The second one considers an orbifold as a singular manifold, the orbit space of a Lie…

We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.

We obtain complete geometric invariants of cobordism classes of oriented simple fold maps of (n+1)-dimensional manifolds into an n-dimensional manifold N in terms of immersions with prescribed normal bundles. We compute that this cobordism…

We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension-2 surgery technique which removes singular strata from…

In this article, we study the mod $\ell$ cohomology of some Deligne-Lusztig varieties for $\operatorname{GL}_n(q)$. We prove that the cohomology groups of these varieties are torsion-free under some conditions on the characteristic. Under…

In this article we prove a generalization of Selberg's lemma on the existence of torsion free, finite index subgroups of arithmetic groups. Some of the geometric applications are the resolution a conjecture of Nimershiem and answers to…

We compute the equivariant bordism of free oriented $(\mathbb{Z}/p)^n$-manifolds as a module over $\Omega_*^{SO}$, when $p$ is an odd prime. We show, among others, that this module is canonically isomorphic to a direct sum of suspensions of…

We prove a Livsic type theorem for cocycles taking values in groups of diffeomorphisms of low-dimensional manifolds. The results hold without any localization assumption and in very low regularity. We also obtain a general result (in any…

This paper investigates conditions under which a given automorphism of a residually torsion-free nilpotent group respects some ordering of the group. For free groups and surface groups, this has relevance to ordering the fundamental groups…