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![The RO(G)-Graded Cohomology of the Equivariant Classifying Space BGSU2 için kapak resmi The RO(G)-Graded Cohomology of the Equivariant Classifying Space BGSU2 için kapak resmi](/client/assets/d79c3e4af2b6d196/ctx/images/no_image.png)
The RO(G)-Graded Cohomology of the Equivariant Classifying Space BGSU2
Başlık:
The RO(G)-Graded Cohomology of the Equivariant Classifying Space BGSU2
Yazar:
Chonoles, Zev, author. (orcid)0000-0003-1307-7384
ISBN:
9780438083189
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (105 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Peter May Committee members: Dylan Wilson.
Özet:
We compute the additive structure of the RO(Cn)-graded Bredon equivariant cohomology of the equivariant classifying space BCnSU(2), for any n that is either prime or a product of distinct odd primes, and we also compute its multiplicative structure for n = 2. In particular, as an algebra over the cohomology of a point, we show that the cohomology of BC2SU(2) is generated by two elements subject to a single relation: writing sigma for the sign representation of C2 in RO(C2), the generators are an element c in dimension 4 sigma and an element C in dimension 4 + 4 sigma, satisfying the relation c2 = epsilon 4 c + x2 C, where epsilon and xi are elements of the cohomology of a point. Throughout, we take coefficients in the Burnside ring Mackey functor A.
The key tools used are equivariant "even-dimensional freeness" and "multiplicative comparison" theorems for G-cell complexes, both proven by Lewis in [Lew88] and subsequently refined by Shulman in [Shu10], and with the former theorem extended by Basu and Ghosh in [BG16]. The latter theorem enables us to compute the multiplicative structure of the cohomology of BC2SU(2) by embedding it in a direct sum of cohomology rings whose structure is more easily understood. Both theorems require the cells of the G-cell complex to be attached in a well-behaved order, and a significant step in our work is to give BCnSU(2) a satisfactory Cn-cell complex structure.
Notlar:
School code: 0330
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(688644.1) | 688644-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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