On the $C_p$-equivariant dual Steenrod algebra

Sankar, Krishanu; Wilson, Dylan

doi:10.48550/arxiv.2103.16006

Cited by 1 publication

(1 citation statement)

References 7 publications

(9 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The computation of H ⋆ (B C 4 Σ 2+ ; F 2 ) also serves for a test case of RO(G) homology computations for equivariant classifying spaces where G is not of prime order. We refer the reader to [Shu14], [Cho18], [Wil19], [SW21] for such computations in the G = C p case.…”

Section: Introductionmentioning

confidence: 99%

The $RO(C_4)$ cohomology of the infinite real projective space

Georgakopoulos¹

2021

Preprint

View full text Add to dashboard Cite

Following the Hu-Kriz method of computing the C 2 genuine dual Steenrod algebra (H F 2 ) ⋆ (H F 2 ), we calculate the C 4 equivariant Bredon cohomology of the classifying space R P ∞ρ = B C 4 Σ 2 as an RO(C 4 ) graded Greenfunctor. We prove that as a module over the homology of a point (which we also compute), this cohomology is not flat. As a result, it can't be used as a test module for obtaining generators in (H F 2 ) ⋆ (H F 2 ) as Hu-Kriz do in the C 2 case. Contents 1. Introduction Acknowledgment 2. Conventions and notations 3. The Tate diagram for C 2 and C 4 3.1. The Tate diagram for C 2 3.2. The RO(C 4 ) homology of a point 3.3. The Tate diagram for C 4 4. Equivariant classifying spaces 4.1. The case of C 2 5. The cohomology of B C 4 Σ 2 6. A cellular decomposition of B C 4 Σ 2 6.1. A decomposition using trivial spheres 7. The spectral sequence for B C 4 Σ 2 7.1. The E 1 page 7.2. The d 1 differentials 7.3. Bottom level computation 7.4. Middle level computation 7.5. Top level differentials 7.6. Coherent lifts 7.7. Top level generators 7.8. Mackey functor structure 7.9. Top level module relations 7.10. Top level cup products Appendix A. Pictures of the spectral sequence Appendix B. The RO(C 4 ) homology of a point in F 2 coefficients B.1. k * S nσ+mλ B.2. k * S −nσ−mλ B.3. k * S mλ−nσ B.4. k * S nσ−mλ B.5. Subtleties about quotients 1 4

show abstract

Section: Introductionmentioning

confidence: 99%

The $RO(C_4)$ cohomology of the infinite real projective space

Georgakopoulos¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

On the $C_p$-equivariant dual Steenrod algebra

Cited by 1 publication

References 7 publications

The $RO(C_4)$ cohomology of the infinite real projective space

The $RO(C_4)$ cohomology of the infinite real projective space

Contact Info

Product

Resources

About