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

Nick Georgakopoulos

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

Algebraic Topology 2021-04-26 v2

Authors: Nick Georgakopoulos

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.

Keywords

ro(c4) homology green functor euler class orientation class c4-representations computer program

Cite

@article{arxiv.1912.06758,
  title  = {The $RO(C_4)$ integral homology of a point},
  author = {Nick Georgakopoulos},
  journal= {arXiv preprint arXiv:1912.06758},
  year   = {2021}
}

Comments

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

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

Abstract

Keywords

Cite

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