Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The limit this contains homeomorphic copy $X$ that is strong deformation retract. We provide method approximate the homology groups and other algebraic invariants. Finally, study computational aspects implementation method.

n the present work, isolation and identification of some plant beneficial bacteria vermicompost were conducted. A total ten bacterial isolates selected characterized morphologically biochemically. Molecular characterization using 16S rRNA gene sequence analysis phylogenic tree According to percentages homology with closest NCBI strain, all belonged six species (

For an extension of associative algebras B ⊂ A over a field and A-bimodule X, we obtain Jacobi–Zariski long nearly exact sequence relating the Hochschild homologies B, relative homology, all them with coefficients in X. This is twice three. There spectral which converges to gap exactness.

The words “spectral sequence” strike fear into the hearts of many hardened mathematicians. These notes will attempt to demonstrate that spectral sequences are not so scary, and also very powerful. This is an unfinished handout for my algebraic topology class. In particular I did not have time to reproduce here the little spectral sequence diagrams showing where all the arrows go. For a comprehe...

We introduce a new approach to determining the structure of topological cyclic homology by means descent spectral sequence. carry out computation for p-adic local field with $${{\mathbb {F}}_p}$$ -coefficients, including case $$p=2$$ which was only covered motivic methods except in totally unramified case.

We construct a covering of Culler-Vogtmann Outer space by the Teichmüller spaces of punctured surfaces. By considering the equivariant homology for the action of Out(Fn) on this covering, we construct a spectral sequence converging to the homology of Out(Fn) that has E terms given by the homology of mapping class groups and groups that are, up to finite index, subgroups of mapping class groups....

We construct a covering of the spine of Culler-Vogtmann Outer space by complexes of ribbon graphs. By considering the equivariant homology for the action of Out(Fn) on this covering, we construct a spectral sequence converging to the homology of Out(Fn) that has its E terms given by the homology of mapping class groups and their subgroups. This spectral sequence can be seen as encoding all of t...

Monopole Floer Homology, Link Surgery, and Odd Khovanov Homology Jonathan Michael Bloom We construct a link surgery spectral sequence for all versions of monopole Floer homology with mod 2 coefficients, generalizing the exact triangle. The spectral sequence begins with the monopole Floer homology of a hypercube of surgeries on a 3-manifold Y , and converges to the monopole Floer homology of Y i...

We construct a covering of the spine of the Culler–Vogtmann outer space Out(F n) by complexes of ribbon graphs. By considering the equivariant homology for the action of Out(F n) on this covering, we construct a spectral sequence converging to the homology of Out(F n) that has its E 1 terms given by the homology of mapping class groups and their subgroups. This spectral sequence can be seen as ...

InterWeaver is a web server for discovering potential protein interactions with online evidence automatically extracted from protein interaction databases, literature abstracts, domain fusion events and domain interactions. Given a new protein sequence, the server identifies potential interaction partners using two approaches. In the homology-based approach, the system performs sequence homolog...