A Vietoris mapping theorem for homotopy

A Vietoris Mapping Theorem for Homotopy

Let X and Y be compact metric spaces and let a map /: X—> Y be onto. The Vietoris Mapping Theorem as proved by Vietoris [8] states that if for all Ofkrfkn-1 and all yEY, flr(/_1(y)) =0 (augmented Vietoris homology mod two) then the induced homomorphism /*: Hr(X)-+Hr(Y) is an isomorphism onto for rfkn — l and onto for r=n. Begle [l; 2] has generalized this theorem to nonmetric spaces and more ge...

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

Exactness of the Mayer-Vietoris Sequence in Homotopy Type Theory

∗This research was sponsored in part by the National Science Foundation under grant numbers CCF-1116703 and CCF-1445995 (REU). The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. See http://homotopytype...

Witt Cohomology, Mayer-vietoris, Homotopy Invariance and the Gersten Conjecture

We establish a Mayer-Vietoris long exact sequence for Witt groups of regular schemes. We also establish homotopy invariance for Witt groups of regular schemes. For this, we introduce Witt groups with supports using triangulated categories. Subsequently we use these results to prove the Gersten-Witt Conjecture for semi-local regular rings of geometric type over infinite fields of characteristic ...

A Homotopy Theorem for Matroids, Ii