Related papers: A variation on the homological nerve theorem

Using Morse theory and a new relative homological linking of pairs, we prove a ``homological linking principle'', thereby generalizing many well known results in critical point theory.

We prove an extension to the simplicial Nerve Lemma which establishes isomorphism of persistent homology groups, in the case where the covering spaces are filtered. While persistent homology is now widely used in topological data analysis,…

We study \L o\'s's theorem in a choiceless context. We introduce some variants of \L o\'s's theorem. These variants seem weaker than \L o\'s's theorem, but we prove that these are equivalent to \L o\'s's theorem.

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We present a relative form of the Toponogov comparison theorem.

We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

It is shown that if T is a connected nontrivial graph and X is an arbitrary finite simplicial complex, then there is a graph G such that the complex Hom(T,G) is homotopy equivalent to X. The proof is constructive, and uses a nerve lemma.…

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

In this note we explain that homotopy coherent simplicial nerve has to used intead of the standard definition in the author's papers on formal deformation theory. A convenient version of the notion of fibered category is presented which is…

Our aim is to compare three nerve functors for strict $n$-categories: the Street nerve, the cellular nerve and the multi-simplicial nerve. We show that these three functors are equivalent in some appropriate sense. In particular, the…

We prove a local version of the Mazur-Ulam theorem.

Further experiments showed the incorrectness of proposed interpretation.

A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…

We make the first step towards a "nerve theorem" for graphs. Let $G$ be a simple graph and let $\mathcal{F}$ be a family of induced subgraphs of $G$ such that the intersection of any members of $\mathcal{F}$ is either empty or connected. We…

We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in…

A version of Jonsson's theorem, as previously generalized, holds in non-modular varieties.

A very short proof of Kneser's theorem via transversal is given.

New version, including a variant of Quillen's proof of the Solomon-Tits theorem.