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    Title      l  On the free rank of abelian groups acting freely on products of spheres
    Author   l  Jin Hong Kim
    Date   l  2013-09-06
    Category   l  ASARC-Prepint-13-04
    Download    l 1404110085_0.639637.pdf  
Abstract
The aim of this paper is to affirmatively resolve a long-standing conjecture
in algebraic topology, related to the free p-rank of abelian groups acting
freely on products of spheres. To be precise, let (Z=p)^r act freely on
S^n1 ×S^n2 ×· · ·×S^nl for a prime p and let l_o denote the number of odd dimensional
spheres in the product of spheres. In this paper we show that,
if p is odd prime, then r is less than or equal to l_o and the free p-rank
of S^n1 × S^n2 × · · · × S^nl is equal to l_o. On the other hand, if p is equal
to 2, it is shown that r is less than or equal to l and the free p-rank of
S^n1 ×S^n2 ×· · ·×S^nl is equal to l.

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