The cohomological index of free $\Z/p$actions is not additive with respect to join
Abstract
Let $p$ denote an odd prime. We show by example that the inequalities obtained in arXiv:1704.05827 for the behaviour of the cohomological index of a join of free $\Z/p$actions are sharp. Namely, for all odd integers $k,l$ at least one of which is greater than one, we give examples of finite free $\Z/p$CW complexes of cohomological indices $k$ and $l$ whose join has index $k+l+1$ and also examples where the join has index $k+l1$.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.06378
 arXiv:
 arXiv:2012.06378
 Bibcode:
 2020arXiv201206378G
 Keywords:

 Mathematics  Algebraic Topology;
 55M35
 EPrint:
 7 pages