Related papers: Homologies are infinitely complex

We compare the smooth and deformation equivalence of actions of finite groups on K3-surfaces by holomorphic and anti-holomorphic transformations. We prove that the number of deformation classes is finite and, in a number of cases, establish…

We show that every orientable infinite-type surface is properly rigid as a consequence of a more general result. Namely, we prove that if a homotopy equivalence between any two non-compact orientable surfaces is a proper map, then it is…

We show that for a gradable finite dimensional algebra the perfect complexes and bounded derived category cannot be distinguished by homotopy invariants.

We extend the notion of an almost flat bundle over a closed Riemannian manifold to bundles over simplicial complexes, and prove that up to a constant factor, this notion is invariant under pullback via maps which induce isomorphisms on…

In this paper, we show that an irreducible proper complex equifocal submanifold of codimension greater than one in a symmetric space of non-compact type. The proof is performed by showing the homogeneity of the lift of the complexification…

The Torelli group $\mathcal T(X)$ of a closed smooth manifold $X$ is the subgroup of the mapping class group $\pi_0(\mathrm{Diff}^+(X))$ consisting of elements which act trivially on the integral cohomology of $X$. In this note we give…

In this paper we extend Y.Eliashberg's $h$-principle to arbitrary generic smooth maps of smooth manifolds. Namely, we prove a necessary and sufficient condition for a continuous map of smooth manifolds of the same dimension to be homotopic…

We prove that, for any infinite-type surface $S$, the integral homology of the closure of the compactly-supported mapping class group $\overline{\mathrm{PMap}_c(S)}$ and of the Torelli group $\mathcal{T}(S)$ is uncountable in every positive…

For any natural $d \ge k \ge 2$ we calculate the cohomology groups of the space of homogeneous polynomials $R^2 \to R$ of degree $d$, which do not vanish with multiplicity $\ge k$ on real lines. For $k=2$ this problem provides the simplest…

In response to a question raised by Belolipetsky and the first author, we prove that for every finite group $G$ there are infinitely many isomorphism classes of compact complex hyperbolic $2$-manifolds with automorphism group isomorphic to…

Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory,…

We investigate the homogeneity of certain kind of slices of the complete complexification of a proper complex equifocal submanifold in a symmetric space of non-compact type.

We show that uniformly finite homology of products of $n$ trees vanishes in all degrees except degree $n$, where it is infinite dimensional. Our method is geometric and applies to several large scale homology theories, including almost…

We study natural additional structures on real algebraic surfaces with trivial first homology mod 2 of the complexification. If the set of real points realizes the zero of the second homology mod 2 of the complexification, then the set of…

We show that if a closed oriented $n$-manifold $M$ has a non-trivial cohomology class of even degree $k$, whose all pullbacks to products of type $S^1\times N$ vanish, then the topological complexity $\mathrm{TC}(M)$ is at least $6$, if $n$…

We introduce certain homology and cohomology subgroups for any almost complex structure and study their pureness, fullness and duality properties. Motivated by a question of Donaldson, we use these groups to relate J-tamed symplectic cones…

As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…

Various curve complexes with vertices representing multicurves on a surface $S$ have been defined, for example [3], [4] and [8]. The homology curve complex $\mathcal{HC}(S,\alpha)$ defined in [7] is one such complex, with vertices…

We prove that every finite connected simplicial complex has the homology of the classifying space for some $\mathrm{CAT}(0)$ cubical duality group. More specifically, for any finite simplicial complex $X$, we construct a locally…

Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the…