Related papers: A variation on the homological nerve theorem

We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.

It gives some new forms of General Neron Desingularization and new applications.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of…

We show that the nerve complex of n arcs in the circle is homotopy equivalent to either a point, an odd-dimensional sphere, or a wedge sum of spheres of the same even dimension. Moreover this homotopy type can be computed in time O(n log…

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

In this article we give a result obtained of an experimental way for the Euler totient function.

A cohomology theory for lambda-rings is developed. This is then applied to study deformations of lambda-rings.

We prove a comparison isomorphism between singular cohomology and sheaf cohomology.

We give a revised version of Schmidt's treatment of forms in many variables, which allows us to prove a Hasse principle under more lenient conditions on the number of variables than what had previously been thought possible with these…

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

We proved three theorems of $S$-version of the mulyiplicity one.

A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.

We develop an axiomatic framework for persistent homology in any degree. We prove the existence and uniqueness for both a persistent version of the Eilenberg-Steenrod axioms for classical homology and a reduced version of this set of…

In this article we show that some recent results on the existence of best proximity points can be obtained from the same result in fixed point theory.

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

We notice new Hermitian counterpart of Swanson's Hamiltonian.

We give a short, geometric proof of Graham's theorem on positivity in the equivariant cohomology of a flag variety, based on a transversality argument.

We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .