Homotopy colimits of classifying spaces of finite abelian groups
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- Tez No: 800093
- Danışmanlar: Belirtilmemiş.
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2014
- Dil: İngilizce
- Üniversite: The Unıversıty Of Brıtısh Columbıa
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
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Özet (Çeviri)
The classifying space BG of a topological group G can be filtered by a sequence of subspaces B(q, G), q ≥ 2, using the descending central series of free groups. If G is finite, describing them as homotopy colimits is convenient when applying homotopy theoretic methods. In this thesis we introduce natural subspaces B(q, G)p ⊂ B(q, G) defined for a fixed prime p. We show that B(q, G) is stably homotopy equivalent to a wedge sum of B(q, G)p as p runs over the primes dividing the order of G. Colimits of abelian groups play an important role in understanding the homotopy type of these spaces. Extraspecial p–groups are key examples, for which these colimits turn out to be finite. We prove that for extraspecial p–groups of rank r ≥ 4 the space B(2, G) does not have the homotopy type of a K(π, 1) space thus answering in a negative way a question which appears in [1]. Furthermore, we give a group theoretic condition, applicable to symmetric groups and general linear groups, which implies the space B(2, G) not having the homotopy type of a K(π, 1) space. For a finite group G, we compute the complex K–theory of B(2, G) modulo torsion.
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