2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74391Suppose that $(Φ, M^n)$ is a smooth $({\Bbb Z}_2)^k$-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 $\dim M^n>2^k\dim F$ and each $p$-dimensional part $F^p$ possesses the linear independence property, then $(Φ, M^n)$ bounds equivariantly, and in particular, $2^k\dim F$ is the best possible upper bound of $\dim M^n$ if $(Φ, M^n)$ is nonbounding.11 pagesAlgebraic Topology57R85, 57S17, 55N22text