相关论文: Toric spaces and face enumeration on simplicial ma…
In this paper, we do the two things. 1. We present a formula to compute the rational cohomology ring of a real topological toric manifold, and thus that of a small cover or a real toric manifold, which implies the formula of Suciu and…
We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that…
We study rational homology groups of one-point compactifications of spaces of complex monic polynomials with multiple roots. These spaces are indexed by number partitions. A standard reformulation in terms of quotients of orbit arrangements…
We study a class of smooth torus manifolds whose orbit space has the combinatorial structure of a simple polytope with holes. We construct moment angle manifolds for such polytopes with holes and use them to prove that the associated torus…
We provide a notion of algebraic rational cell with applications to intersection theory on singular varieties with torus action. Based on this notion, we study the algebraic analogue of $\mathbb{Q}$-filtrable varieties: algebraic varieties…
We present some classification results for quasitoric manifolds (M) with (p_1(M)=-\sum a_i^2) for some (a_i\in H^2(M)) which admit an action of a compact connected Lie-group (G) such that (\dim M/G \leq 1). In contrast to Kuroki's work we…
An upper bound is obtained on the rank of a torus which can act smoothly and effectively on a smooth, closed, simply connected, rationally elliptic manifold. In the maximal-rank case, the manifolds admitting such actions are classified up…
An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden,…
This thesis addresses the theory of topological spaces and the foundations of persistence theory. We will discuss chain complexes and the associated simplicial homology groups, as well as their relationship with singular homology theory.…
In this paper, we compute contact homology of some quasi-regular contact structures, which admit Hamiltonian actions of Reeb type of Lie groups. We will discuss the toric contact case, (where the torus is of Reeb type), and the case of…
We generalize a theorem of Delzant classifying compact connected symplectic manifolds with completely integrable torus actions to certain singular symplectic spaces. The assumption on singularities is that if they are not finite quotient…
The project of Greenlees et al. on understanding rational G-spectra in terms of algebraic categories has had many successes, classifying rational G-spectra for finite groups, SO(2), O(2), SO(3), free and cofree G-spectra as well as rational…
M. Kontsevich proposed a topological construction for an invariant Z of rational homology 3-spheres using configuration space integrals. G. Kuperberg and D. Thurston proved that Z is a universal real finite type invariant for integral…
We construct all possible Hamiltonian torus actions for which all the non-empty reduced spaces are two dimensional (and not single points) and the manifold is connected and compact, or, more generally, the moment map is proper as a map to a…
It is well-known that the basic modal logic of all topological spaces is $S4$. However, the structure of basic modal and hybrid logics of classes of spaces satisfying various separation axioms was until present unclear. We prove that modal…
In 2006 Masuda and Suh asked if two compact non-singular toric varieties having isomorphic cohomology rings are homeomorphic. In the first part of this paper we discuss this question for topological generalizations of toric varieties,…
We associate a root system to a finite set in a free abelian group and prove that its irreducible subsystem is of type A, B or D. We apply this general result to a torus manifold, where a torus manifold is a $2n$-dimensional connected…
We examine the integral cohomology rings of certain families of $2n$-dimensional orbifolds $X$ that are equipped with a well-behaved action of the $n$-dimensional real torus. These orbifolds arise from two distinct but closely related…
We find the complete rational homology for the finite subset spaces of a $d$-dimensional sphere. We also determine the integral homology in top $d$ degrees and obtain a partial description of it in codimension $d$.
This paper is a survey of recent advances as well as open problems in the study of face numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed range from neighborliness of centrally symmetric polytopes and the…