Related papers: A variation on the homological nerve theorem
Theory of $n$-complements with applications is presented.
We provide new sufficient conditions under which Ryser's conjecture holds.
We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a…
We give a simple proof that complete Segal animae are equivalent to categories.
We show that the complicial nerve construction is homotopically compatible with two flavors of cone constructions when starting with an $\omega$-category that is suitably free and loop-free. An instance of the result recovers the fact that…
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
The analogue of Goldie's Theorem for prime rings is proved for rings graded by abelian groups, eliminating unnecessary additional hypotheses used in earlier versions.
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch…
We prove that a contractible orbifold is a manifold.
We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.
In this paper we provide an application to the Neumann problem of a recent three critical points theorem.
We show that asymptotic equivalence, in a strong form, holds between two random graph models with slightly differing edge probabilities under substantially weaker conditions than what might naively be expected. One application is a simple…
We prove an extension of the Quillen Theorem Bn for homotopy fibres to a similar result for homotopy pullbacks and use this to obtain sufficient conditions on a pullback diagram of categories to guarantee that it be a homotopy pullback.
The purpose of this note is to extend to Brownian loops some homology and holonomy results obtained in the case of discrete loops on a graph
We give empirical evidence that the UV-divergences of a renormalizable field theory are knot invariants.
We point out a simple characterisation of topological amenability in terms of bounded cohomology, following Johnson's reformulation of amenability.
We present a selection of known as well as new variants of the Sensitivity Conjecture and point out some weaker versions that are also open.
We present here a simple and direct proof of the classic geometric version of Hahn-Banach Theorem from its analitic version, in the real case. The reciprocal implication, and the direct proofs of both versions, are already well kown, but…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…