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Authors:Zhi Lü  
Affiliation:Institute of Mathematics, Fudan University, Shanghai, 200433, People's Republic of China
Abstract:Suppose that $(Phi, M^n)$ is a smooth $({mathbb Z}_2)^k$-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 $dim M^n>2^kdim F$ and each $p$-dimensional part $F^p$ possesses the linear independence property, then $(Phi, M^n)$ bounds equivariantly, and in particular, $2^kdim F$ is the best possible upper bound of $dim M^n$ if $(Phi, M^n)$ is nonbounding.

Keywords:$({mathbb{Z}}_2)^k$-action   equivariant cobordism   linear independence condition
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