(\Bbb Z₂)^k-actions with w(F)=1

2005/03/05 by Zhi Lü
Mathematics · #math.AT #msc:57R85 #msc:57S17 #msc:55N22

paper · pdf

published as Proc. Amer. Math. Soc. 133 (2005), 3721-3733. · 11 pages

arxiv created 2005/03/05 · arxiv updated 2009/12/01

Abstract

Suppose that (Φ, Mⁿ) is a smooth (\Bbb Z₂)^k-action on a closed smooth n-dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each connected component of the fixed point set F vanish in positive dimension. This paper shows that if dim Mⁿ>2^kdim F and each p-dimensional part F^p possesses the linear independence property, then (Φ, Mⁿ) bounds equivariantly, and in particular, 2^kdim F is the best possible upper bound of dim Mⁿ if (Φ, Mⁿ) is nonbounding.

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