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arXiv · 2403.07102

Homotopy type of shellable $q$-complexes and their homology groups

Sudhir R. Ghorpade·Rakhi Pratihar·Tovohery H. Randrianarisoa·Hugues Verdure·Glen Wilson
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Abstract

The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for $q$-simplicial complexes, recent work of Ghorpade, Pratihar, and Randrianarisoa extends the study of shellability to $q$-matroid complexes and determines singular homology groups for a subclass of these $q$-simplicial complexes. In this paper, we determine the homotopy type of shellable $q$-simplicial complexes. Moreover, we establish the shellability of order complexes from lexicographically shellable $q$-simplicial complexes, that include the $q$-matroid complexes. This results in a comprehensive determination of the homology groups for any lexicographically shellable $q$-complexes.

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Sudhir R. Ghorpade, Rakhi Pratihar, Tovohery H. Randrianarisoa, Hugues Verdure, Glen Wilson. 2024-03-11. Homotopy type of shellable $q$-complexes and their homology groups. https://arxiv.org/abs/2403.07102

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