Generalized Mayer-Vietoris sequences in algebraic K-theory

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•,• ...

Mayer-vietoris Sequences in Stable Derivators

We show that stable derivators, like stable model categories, admit Mayer-Vietoris sequences arising from cocartesian squares. Along the way we characterize homotopy exact squares, and give a detection result for colimiting diagrams in derivators. As an application, we show that a derivator is stable if and only if its suspension functor is an equivalence.

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...

The Mayer-vietoris Sequence for Generalized Homology Theories

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 ...