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Results tagged with homology
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user 4194
Homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
3
votes
Accepted
Algorithm that decreases the size of the simplicial triangulation
There are a number of papers out there for efficient computation of homology of simplicial complexes; I enjoyed reading this paper by Dumas, Heckenbach, Saunders and Welker, but I don't know how authoritative … For actual computations of homology groups of simplicial complexes, I would suggest using software from CHomP; it's pretty fast in my experience, much faster than code which just uses a generic Smith normal …
- 4,254
14
votes
Accepted
How to triangulate real projective spaces (as simplicial complexes in Mathematica)?
If you want code, see the patch for Sage at http://trac.sagemath.org/sage_trac/attachment/ticket/9125/trac_9125-projective-space.patch. This patch also includes references for triangulations of $\mat …
- 4,254
1
vote
Amending flawed "proof" that homology groups are zero
Edit: this is answering the wrong question (coprime subsets rather than coprime-free subsets), but in case it's useful, I will leave it here.
I believe that this simplicial complex should be a simplex …
- 4,254
15
votes
Accepted
Massey Products vs. $A_\infty$-Structures
When $n=3$, this is in Stasheff's H-spaces from a homotopy point of view, Chapter 12. For general $n$, it is in a paper of mine with Lu, Wu, and Zhang, "$A_\infty$-structures in Ext algebras, J. Pure …
- 4,254