The $RO(C_4)$ integral homology of a point

Abstract

We compute the $RO(C_4)$ integral homology of a point with complete information as a Green functor, and we show that it is generated, in a slightly generalized sense, by the Euler and orientation classes of the irreducible real $C_4$-representations. We have devised a computer program that automates these computations for groups $G=C_{p^n}$ and we have used it to verify our results for $G=C_4$ in a finite range.

Comments are most welcome! 42 pages. The code can be found on: https://github.com/NickG-Math/Mackey . Updates: Added conjecture for all power 2 cyclic groups, added discussion on the new features of the computer program (support for spaces that are not points, sparse matrices, equivariant algebraic Morse theory), other minor improvements

References in corpus (1)

• Chain complex reduction via fast digraph traversal

Cited by in corpus (3)

• Derived Mackey functors and $C_{p^n}$-equivariant cohomology
• The $RO(C_4)$ cohomology of the infinite real projective space
• $C_2$ equivariant characteristic classes over the rational Burnside ring