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Computing Cohomology of Unordered Configuration Spaces of Manifolds
Başlık:
Computing Cohomology of Unordered Configuration Spaces of Manifolds
Yazar:
Maguire, Megan, author.
ISBN:
9780438133624
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (97 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Melanie Matchett Wood Committee members: Autumn E. Kent; Laurentiu G. Maxim; Steven Sam.
Özet:
We give a concrete method to explicitly compute the rational cohomology of the unordered configuration spaces of connected, oriented, closed, even-dimensional manifolds of finite type which has been implemented in Sage. As an application, we give a complete computation of the stable and unstable rational cohomology of unordered configuration spaces in some cases, including that of CP3 and a genus 1 Riemann surface, which is equivalently the homology of the elliptic braid group. In an appendix, we also give large tables of unstable and stable Betti numbers of unordered configuration spaces. From these, we empirically observe stability phenomenon in the unstable cohomology of unordered configuration spaces of some manifolds, some of which we prove and some of which we state as conjectures. We also prove that there is a uniform bound on the degree in which cohomology algebras of unordered configuration spaces of two classes of manifolds are generated as algebras, namely connected, orientable manifolds with no odd cohomology.
Notlar:
School code: 0262
Konu Başlığı:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(696090.1) | 696090-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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