Top homology of hypergraph matching complexes, p-cycle complexes and Quillen complexes of symmetric groups

John Shareshian, Michelle L. Wachs

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We investigate the representation of a symmetric group Sn on the homology of its Quillen complex at a prime p. For homology groups in small codimension, we derive an explicit formula for this representation in terms of the representations of symmetric groups on homology groups of p-uniform hypergraph matching complexes. We conjecture an explicit formula for the representation of Sn on the top homology group of the corresponding hypergraph matching complex when n ≡ 1 mod p. Our conjecture follows from work of Bouc when p = 2, and we prove the conjecture when p = 3.

Original languageEnglish (US)
Pages (from-to)2253-2271
Number of pages19
JournalJournal of Algebra
Volume322
Issue number7
DOIs
StatePublished - Oct 1 2009

Keywords

  • Matching complex
  • Quillen complex
  • Symmetric group

ASJC Scopus subject areas

  • Algebra and Number Theory

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