Z_2^k-actions with connected fixed point set - Costa, Jessica C. R. R.; Pergher, Pedro L. Q.; Moraes, Renato M. (Topological Methods in Nonlinear Analysis, 2023)
In this paper we describe the equivariant cobordism classification of smooth actions (M^m,φ) of the group G=Z_2^k on closed smooth m-dimensional manifolds M^m, for which the fixed point set of the action is a connected manifold of dimension n and 2^k n - 2^k-1 ≤ m < 2^k n. Here, Z_2^k is considered as the group generated by k commuting smooth involutions defined on M^m. This generalizes a previous result of 2008 of the second author, who obtained this type of classification for k=2 and m=4n-1 or m=4n-2.