Corpus ID: 237940243

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

```@inproceedings{Basu2021EquivariantHD,
title={Equivariant homology decompositions for cyclic group actions on definite 4-manifolds},
author={Samik Basu and Pinka Dey and Aparajita Karmakar},
year={2021}
}```
• Samik Basu
• Published 27 September 2021
• Mathematics
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…

#### References

SHOWING 1-10 OF 19 REFERENCES
Non-trivial extensions in equivariant cohomology with constant coefficients
• Samik Basu, Surojit Ghosh
• Mathematics
• 2021
In this paper, we prove some computational results about equivariant cohomology over the cyclic group Cpn of prime power order. We show that there is an inductive formula when the dimension of the
A freeness theorem for RO(Z/2)-graded cohomology
Abstract In this paper it is shown that the RO ( Z / 2 ) -graded cohomology of a certain class of Rep ( Z / 2 ) -complexes, which includes projective spaces and Grassmann manifolds, is always free as
THE RO(C2)-GRADED COHOMOLOGY OF C2-SURFACES IN Z/2-COEFFICIENTS
• 2019
A surface with an involution can be viewed as a C2-space where C2 is the cyclic group of order two. Up to equivariant isomorphism, all involutions on surfaces were classified in [BCNS] and recently
Equivariant stable homotopy theory
Equivariant homotopy theory started from geometrically motivated questions about symmetries of manifolds. Several important equivariant phenomena occur not just for a particular group, but in a
The RO(G)-graded equivariant ordinary cohomology of complex projective spaces with linear ℤ/p actions
INTRODUCTION. If X is a CW complex with cells only in even dimensions and R is a ring, then, by an elementary result in cellular cohomology theory, the ordinary eohomology H*(X;R) of X with R
The equivariant Hurewicz map
Let G be a compact Lie group, Y be a based G-space, and V be a G-representation. If π V G (Y) is the equivariant homotopy group of Y in dimension V and H V G (Y) fis the equivariant ordinary homology
Equivariant cohomology for cyclic groups of square-free order
• Mathematics
• 2020
The main objective of this paper is to compute \$RO(G)\$-graded cohomology of \$G\$-orbits for the group \$G=C_n\$, where \$n\$ is a product of distinct primes. We compute these groups for the constant
The RO(G)-graded equivariant ordinary homology of G-cell complexes with even-dimensional cells for G=Z/p
• Mathematics
• 2004
Part 1. The Homology of \$\mathbb{Z}/p\$-Cell Complexes with Even-Dimensional Cells: Preliminaries The main freeness theorem (Theorem 2.6) An outline of the proof of the main freeness result (Theorem
A structure theorem for RO(C2)–graded Bredon cohomology
Let \$C_2\$ be the cyclic group of order two. We present a structure theorem for the \$RO(C_2)\$-graded Bredon cohomology of \$C_2\$-spaces using coefficients in the constant Mackey functor
PERMUTATIONS
• 1994
Permutations of finite sets play a central role in algebraic and enumerative combinatorics. In addition to having many interesting enumerative properties per se, permutations also arise in almost