Related papers: A variation on the homological nerve theorem

In this note we show that a particular homological nerve theorem, which was originally proved for a finite cover of a simplicial complex by subcomplexes, also holds for an open cover of an arbitrary topological space. The motivation for…

The nerve theorem is a basic result of algebraic topology that plays a central role in computational and applied aspects of the subject. In topological data analysis, one often needs a nerve theorem that is functorial in an appropriate…

A vector variational principle is proved.

The Nerve Theorem relates the topological type of a suitably nice space with the nerve of a good cover of that space. It has many variants, such as to consider acyclic covers and numerous applications in topology including applied and…

The paper presents a counterexample to the Hodge conjecture.

Given a locally finite cover of a simplicial complex by subcomplexes, Bj\"orner's version of the Nerve Theorem provides conditions under which the homotopy groups of the nerve agree with those of the original complex through a range of…

We prove a variation of Gronwall's lemma.

A very simple but useful almost sure convergence theorem of probability is given.

We show that a regular cover of a general topological space provides structure similar to a triangulation. In this general setting we define analogues of simplicial maps and prove their existence and uniqueness up to homotopy. As an…

Given a simplicial complex and a collection of subcomplexes covering it, the nerve theorem, a fundamental tool in topological combinatorics, guarantees a certain connectivity of the simplicial complex when connectivity conditions on the…

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

An technically interesting proof of a known theorem.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

We obtain some results related to Romanoff's theorem.

Two of the most useful tools in topological combinatorics are the nerve lemma and discrete Morse theory. In this note we introduce a theorem that interpolates between them and allows decompositions of complexes into non-contractible pieces…

A variation on the splitting principle

We give a new simpler proof of a theorem of Jayne and Rogers.

In this note a far extension of the Banach fixed point theorem is proved.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

We prove properness of (co)Cartesian fibrations as well as a straightening and unstraightening equivalence, which is compatible with cartesian products, when the base is the nerve of a small category.