Homotopy type of shellable $q$-complexes and their homology groups
Combinatorics
2024-03-13 v1
Abstract
The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for -simplicial complexes, recent work of Ghorpade, Pratihar, and Randrianarisoa extends the study of shellability to -matroid complexes and determines singular homology groups for a subclass of these -simplicial complexes. In this paper, we determine the homotopy type of shellable -simplicial complexes. Moreover, we establish the shellability of order complexes from lexicographically shellable -simplicial complexes, that include the -matroid complexes. This results in a comprehensive determination of the homology groups for any lexicographically shellable -complexes.
Keywords
Cite
@article{arxiv.2403.07102,
title = {Homotopy type of shellable $q$-complexes and their homology groups},
author = {Sudhir R. Ghorpade and Rakhi Pratihar and Tovohery H. Randrianarisoa and Hugues Verdure and Glen Wilson},
journal= {arXiv preprint arXiv:2403.07102},
year = {2024}
}
Comments
25 pages