A note on free actions of groups on products of spheres

Authors

  • J. H. Jo Sogang University
  • J. B. Lee Sogang University

Keywords:

CW-complex, free action, free rank, solvmanifolds, strongly polycyclic groups

Abstract

It has been conjectured that if $G = (\bbz_{p})^r$ acts freely on a finite $CW$-complex $X$ which is homotopy equivalent to a product of spheres $S^{n_1} \times S^{n_2} \times \cdots \times S^{n_k}$, then $r \leq k$. We ask the question with the relaxation that $X$ is finite-dimensional, and show that it suffices to consider the case that the dimension of spheres are greater than or equal to $2$ in order to answer the question. 10.1017/S0004972713000130

Author Biographies

J. H. Jo, Sogang University

Department of Mathematics, Associate Professor

J. B. Lee, Sogang University

Department of Mathematics, Professor

Published

2013-08-11

Issue

Vol. 88 No. 2 (2013)

Section

Articles
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