Stratified simplices and intersection homology

Details Stratified simplices and intersection homology Stratified simplices and intersection homology

1998-07-23

arxiv.org/abs/math/9807128v2

Mathematics

Algebraic Topology

Concise statement of topological definitions in `Local global intersection homology', alg-geom/9709011. LaTeX 2e, 8 pages

Scientific paper

Intersection homology is obtained from ordinary homology by imposing conditions on how the embedded simplices meet the strata of a space $X$. In this way, for the middle perversity, properties such as strong Lefschetz are preserved. This paper defines local-global intersection homology groups, that record global information about the singularities of $X$. They differ from intersection homology in that stratified rather than ordinary simplices are used. An example of such is $\sigma_j\times C\sigma_i$, where $\sigma_i$ and $\sigma_j$ are ordinary simplices, and $C$ is the coning operator. The paper concludes with a sketch of the relationship between local-global homology and the geometry of convex polytopes. This paper is a more formal exposition of part of the author's `Local-global intersection homology', alg-geom/9709011.

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