The freeness theorem for equivariant cohomology of Rep(C2)-complexes

Hogle, Eric; May, Clover

doi:10.1016/j.topol.2020.107413

Cited by 2 publications

(2 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Example 3.8. Kronholm and Hogle-May showed that if 𝑋 is a finite 𝑅𝑒𝑝(𝐶 2 )-complex (meaning a 𝐶 2 -complex formed by attaching disks in representations along their boundaries), then 𝑋 has free 𝐻𝔽 2 -homology (with no summands induced up from the trivial group) [23], [18]. Example 3.9.…”

Section: Free and Projectivementioning

confidence: 99%

“…Example Kronholm and Hogle–May showed that if

X

is a finite

Rep(C_2)

‐complex (meaning a

C_2

‐complex formed by attaching disks in representations along their boundaries), then

X

has free

H{\protect \underline{{\mathbb {F}}}}_2

‐homology (with no summands induced up from the trivial group) [23], [18]. …”

Section: Free R$r$‐homologymentioning

confidence: 99%

See 1 more Smart Citation

Freeness and equivariant stable homotopy

Hill

2022

Journal of Topology

View full text Add to dashboard Cite

We introduce a notion of freeness for RO$RO$‐graded equivariant generalized homology theories, considering spaces or spectra E$E$ such that the R$R$‐homology of E$E$ splits as a wedge of the R$R$‐homology of induced virtual representation spheres. The full subcategory of these spectra is closed under all of the basic equivariant operations, and this greatly simplifies computation. Many examples of spectra and homology theories are included along the way. We refine this to a collection of spectra analogous to the pure and isotropic spectra considered by Hill–Hopkins–Ravenel. For these spectra, the RO$RO$‐graded Bredon homology is extremely easy to compute, and if these spaces have additional structure, then this can also be easily determined. In particular, the homology of a space with this property naturally has the structure of a co‐Tambara functor (and compatibly with any additional product structure). We work this out in the example of BUR$BU_{\mathbb {R}}$ and coinduced versions of this. We finish by describing a readily computable bar and twisted bar spectra sequence, giving Bredon homology for various E∞$E_{\infty }$ pushouts, and we apply this to describe the homology of BBUR$BBU_{\mathbb {R}}$.

show abstract

Section: Free and Projectivementioning

confidence: 99%

“…Example Kronholm and Hogle–May showed that if