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(If I remember correctly) a shellable (simplicial) complex automatically has the homotopy type of a wedge of spheres: if you could find a shellable triangulation you should be done. Of course, this'l …

Is there a good way to define a sheaf over a simplicial set - i.e. as a functor from the diagram of the simplicial set to wherever the sheaf takes its values - in a way that while defined on simplex b …

I am trying to compute $H^*(X)$ for a (potentially large, finite, finitely filtered) simplicial complex $X$ using a cover $U_i$ of $X$. I am building chain complexes for $X$ with a simplex that appea …

Is the face poset of a simplicial or nice enough cellular complex a Heyting algebra in some natural way? Edited to add: For the benefit of illustration, here's a few face posets: the boundary of a …

Are there results in algebraic topology -- preferably relating to homology or homotopy or phraseable in simplicial sets -- that are not true in an intuitionistic logic? In other words, are there res …

Robert Ghrist started out his (prolific) research career investigating knotted trajectories in dynamical systems. http://www.math.upenn.edu/~ghrist/preprints-dynamics.html Konstantin Mischaikow has b …

There are several applications and libraries out there that deal with homology computations with various approaches to the computation. One field with a strong focus on efficient computation of homolo …

There is the Aguilar-Gitler-Prieto book on algebraic topology: Algebraic Topology from a Homotopical Viewpoint. As I recall from browsing it, the book is meant to be a graduate course in algebraic top …

There is the idea of a simplicial manifold, which works by checking that the complex is pure (all facets of the same dimension) and that each codimension 1 face is included in the correct number of fa …

Another good place to start is to track the output of Marion Mrozek and Konstantin Mischaikow, and their various co-authors. There is a whole group at the University in Krakow centered on Mrozek doing …

One place where papers on applications of algebraic topology — to dynamical systems as well as to statistics, data analysis, bio-medicine, computational geometry and other areas — gets aggregated is o …

The closest I can find spontaneously would be Matthew Kahle's work on random topology; http://arxiv.org/abs/0910.1649 looks like it would be directly related to your question, and http://arxiv.org/abs …

So, the one 0-cell forces the 1-skeleton to be a figure-8. And we attach three 2-cells to this figure-8. These cells can be attached to: loop 1, with some winding number n. loop 2, with some winding …