Equivariant homology decompositions for cyclic group actions on definite 4-manifolds

2021/09/27 by Basu, Samik, Dey, Pinka, Karmakar, Aparajita
#55N91 #57S17 (Primary) 55P91 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.12874

Abstract

In this paper, we study the equivariant homotopy type of a connected sum of linear actions on complex projective planes defined by Hambleton and Tanase. These actions are constructed for cyclic groups of odd order. We construct cellular filtrations on the connected sum using spheres inside unitary representations. A judicious choice of filtration implies a splitting on equivariant homology for general cyclic groups under a divisibility hypothesis, and in all cases for those of prime power order.

Related

• Finite group actions on 4-manifolds and equivariant bundles
• Equivariant Cohomology of Projective Spaces
• Multiplicative structure in equivariant cohomology
• Equivariant periodic cyclic homology for ample groupoids
• Equivariant K-theory and Resolution II: Non-Abelian actions