THE EULER CLASS OF A SUBSET COMPLEX


Guclukan A., Yalçın E.

QUARTERLY JOURNAL OF MATHEMATICS, vol.61, no.1, pp.43-68, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 61 Issue: 1
  • Publication Date: 2010
  • Doi Number: 10.1093/qmath/han025
  • Journal Name: QUARTERLY JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.43-68
  • Dokuz Eylül University Affiliated: No

Abstract

In this paper, we answer this question completely. We show that zeta(G) is non-zero if and only if G is an elementary abelian p-group or G is isomorphic to Z/9, Z/4 x Z/4 or (Z/2)(n) x Z/4 for some integer n >= 0. We obtain this result by first showing that zeta(G) is zero when G is a non-abelian group, then by calculating zeta(G) for specific abelian groups. The key ingredient in the proof is an observation by Mandell which says that the Ext class of the subset complex delta (G) is equal to the (twisted) Euler class of the augmentation module of the regular representation of G.