Vietoris-Begle theorem for spectral pro-homology

Multicore Homology via Mayer Vietoris

In this work we investigate the parallel computation of homology using the Mayer-Vietoris principle. We present a two stage approach for parallelizing persistence. In the first stage, we produce a cover of the input cell complex by overlapping subspaces. In the second stage, we use this cover to build the Mayer-Vietoris blowup complex, a topological space, which organizes the various subspaces ...

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...

The Mayer-vietoris Sequence for Generalized Homology Theories

A note on spectral mapping theorem

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

The Generalized Mayer-vietoris Principle and Spectral Sequences

This is my spin of the some stuff from from [1]. CONTENTS 1. Double complexes 1 2. The generalized Mayer-Vietoris principle 6 3. Presheaves and sheaves 17 4. The Čech cohomology of presheaves 22 5. Spectral sequences 25 6. The Leray-Serre spectral sequence 32 References 34 1. DOUBLE COMPLEXES Suppose that R is a commutative ring with 1. A double complex of R-modules is a bigraded R-module E•,• ...