Related papers: Fibrations between finite topological spaces

In this paper we characterize [strict] o-boundedness of the free (abelian) topological group F(X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

We prove the existence of minimal models for fibrations between dendroidal sets in the model structure for infinity-operads, as well as in the covariant model structure for algebras and in the stable one for connective spectra. In an…

Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…

Considering non-constant holomorphic maps $\beta_{i}:S_{i}\to S_{0}$, $i\in\{1,2\}$, between non-compact Riemann surfaces for which it is associated its fiber product $S_{1}\times_{(\beta_{1},\beta_{2})}S_{2}$. With this setting, in this…

This (partially expository) paper discusses Lagrangian Floer cohomology in the context of Lefschetz fibrations, with emphasis on the algebraic structures encountered there. In addition to the well-known directed A_infinity algebras which…

Given a manifold $M$ and a proper sub-bundle $\Delta\subset TM$, we study homotopy properties of the horizontal base-point free loop space $\Lambda$, i.e. the space of absolutely continuous maps $\gamma:S^1\to M$ whose velocities are…

For each arbitrary finite group $G$, we consider a suitable notion of Gromov Hausdorff distance between compact $G$ metric spaces and derive lower bounds based on equivariant topology methods. As applications, we prove equivariant rigidity…

Mid-dimensional $(A,B,A)$ and $(B,B,B)$-branes in the moduli space of flat $G_{\mathbb C}$-connections appearing from finite group actions on compact Riemann surfaces are studied. The geometry and topology of these spaces is then described…

We investigate Whitehead's asphericity question from a new perspective, using results and techniques of the homotopy theory of finite topological spaces. We also introduce a method of reduction to investigate asphericity based on the…

This is the author's PhD thesis. It is a contribution to categorical logic, in particular to the theory of realizability toposes. While the tools of categorical logic have proven very successful in analyzing and organizing proof theoretic…

We introduce the higher topological complexity (TC_{n}) of a fibration in two ways: the higher homotopic distance and the Schwarz genus. Then we have some results on this notion related to TC, TC_{n} or cat of a topological space or a…

This survey describes some recent work, by the authors and others, on the existence of algebraic fibrations of group extensions, as well as the finiteness properties of their algebraic fibers, in the realm of both abstract and pro-$p$…

Rationally null-homologous links in Seifert fibered spaces may be represented combinatorially via labeled diagrams. We introduce an additional condition on a labeled link diagram and prove that it is equivalent to the existence of a…

Let $G$ be a topological group and let $K,L\subseteq G$ be closed subgroups, with $K\subseteq L$. We prove that if $L$ is a locally compact pro-Lie group, then the map $q:G/K\to G/L$ is a fibration. As an application of this, we obtain two…

We introduce the notion of tight homomorphism into a locally compact group with nonvanishing bounded cohomology and study these homomorphisms in detail when the target is a Lie group of Hermitian type. Tight homomorphisms between Lie groups…

Assume that there exists a smooth map between two closed manifolds $M^m\to N^k$ with only finitely many cone-like singular points, where $2\leq k\leq m\leq 2k-1$. If $(m,k)\not\in\{(2,2), (4,3), (5,3), (8,5), (16,9)\}$, then $M^m$ admits a…

This paper has two parts. First, we recall and detail the definition of the Grothendieck topos of a connectivity space, that is the topos of sheaves on such a space. In the second part, we prove that every finite connectivity space is…

Given a semistable fibration $f\colon X\to B$ we introduce a correspondence between foliations $\mathcal{F}$ on $X$ and local systems $\mathbb{L}$ on $B$. Building up on this correspondence we find conditions that give maximal rationally…

We establish a compact analog of the P = W conjecture. For a holomorphic symplectic variety with a Lagrangian fibration, we show that the perverse numbers associated with the fibration match perfectly with the Hodge numbers of the total…