On a construction of some homology $d$-manifolds
Biplab Basak, Sourav Sarkar

TL;DR
This paper characterizes homology d-manifolds with g2=3, showing they are spheres obtainable from simpler spheres via joins, retriangulations, and connected sums, extending known classifications for lower g2 values.
Contribution
It provides a combinatorial characterization of homology d-manifolds with g2=3 and describes their construction from spheres with g2≤2.
Findings
Homology d-manifolds with g2=3 are spheres.
These spheres can be constructed from simpler spheres using joins, retriangulations, and connected sums.
Structural results on prime normal d-pseudomanifolds with g2=3.
Abstract
The -vector of a simplicial complex contains a lot of information about the combinatorial and topological structure of that complex. Several classification results regarding the structure of normal pseudomanifolds and homology manifolds have been established concerning the value of . It is known that when , all normal pseudomanifolds of dimensions at least three are stacked spheres. In the cases of and , all homology manifolds are polytopal spheres and can be obtained through retriangulation or join operations from the previous ones. In this article, we provide a combinatorial characterization of the homology -manifolds, where and . These are spheres and can be obtained through operations such as joins, some retriangulations, and connected sums from spheres with . Furthermore, we have presented a structural result on prime normal…
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Commutative Algebra and Its Applications
