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Progress towards the calculation of ...

Blumberg, Andrew J.

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Progress towards the calculation of the K-theory of Thom spectra.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Progress towards the calculation of the K-theory of Thom spectra./
作者:	Blumberg, Andrew J.
面頁冊數:	121 p.
附註:	Source: Dissertation Abstracts International, Volume: 66-03, Section: B, page: 1495.
Contained By:	Dissertation Abstracts International66-03B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3168322
ISBN:	0542040816

Progress towards the calculation of the K-theory of Thom spectra.
Blumberg, Andrew J.

Progress towards the calculation of the K-theory of Thom spectra. - 121 p.

Source: Dissertation Abstracts International, Volume: 66-03, Section: B, page: 1495.

Thesis (Ph.D.)--The University of Chicago, 2005.

This thesis describes three distinct projects. First, we construct a discrete model of the homotopy theory of S1-spaces. We define a category P with objects composed of a simplicial set and a cyclic set along with compatibility data. P inherits a model structure from the model structures on the constituent categories. We show that there is a Quillen equivalence between P and the model category of S1-spaces where weak equivalences and fibrations are maps inducing weak equivalences and fibrations on passage to fixed point sets.

ISBN: 0542040816Subjects--Topical Terms:

515831
Mathematics.

Progress towards the calculation of the K-theory of Thom spectra.
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245 1 0 $a Progress towards the calculation of the K-theory of Thom spectra.
300 $a 121 p.
500 $a Source: Dissertation Abstracts International, Volume: 66-03, Section: B, page: 1495.
500 $a Adviser: Peter May.
502 $a Thesis (Ph.D.)--The University of Chicago, 2005.
520 $a This thesis describes three distinct projects. First, we construct a discrete model of the homotopy theory of S1-spaces. We define a category P with objects composed of a simplicial set and a cyclic set along with compatibility data. P inherits a model structure from the model structures on the constituent categories. We show that there is a Quillen equivalence between P and the model category of S1-spaces where weak equivalences and fibrations are maps inducing weak equivalences and fibrations on passage to fixed point sets.
520 $a Next, we study the category of equivariant diagram spectra indexed on the category WG of based G-spaces homeomorphic to finite G-CW-complexes (G a compact Lie group). We show that there is a model structure on this category which admits a monoidal Quillen equivalence to the category of orthogonal G-spectra. There is a model-theoretic identification of the fibrant objects as functors Z such that for A ∈ WG the collection {Z(A &and; SW)} forms an O-G-prespectrum as W varies over the universe U. We show that a functor is fibrant if and only if it takes G-homotopy pushouts to G-homotopy pullbacks and is compatible with equivariant Atiyah duality for orbit spaces G/H+.
520 $a Finally, we compute the topological Hochschild homology of Thom spectra. For a cofibrant S-algebra R, THH (R) is equivalent to the cyclic bar construction NcycR. When R is an Einfinity-ring spectrum, N cycR &cong; R &otimes; S1. We prove that the Thom spectrum functor M from Einfinity-maps f : X → BG to commutative S-algebras commutes with tensors. Therefore M(f &otimes; S1) &cong; M f &otimes; S1. We construct a symmetric monoidal product &sstarf;L on based L (1)-spaces over BG by mimicking the construction of the smash product &and;L of S-modules. Ainfinity-spaces and Einfinity-spaces are monoids and commutative monoids for &sstarf;L . Thus, an Ainfinity-map f : X → BG induces a composite Ncyc&sstarf;f:&vbm0;N cyc&sstarf;X&vbm0;→&vbm0;N cyc&sstarf;BG&vbm0;→BG where the last map is levelwise multiplication. We show that M is a strong symmetric monoidal functor from based L (1)-spaces to S-modules, which implies that M( Ncyc&sstarf;f ) &cong; NcycMf. There is a comparison between NcycBX and the free loop space ΛBX. We show that under certain hypotheses there is a splitting Ncyc Mf &sime; Mf &and; BX+, allowing us to recover calculations of THH for bordism spectra and H Z /p.
590 $a School code: 0330.
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710 2 0 $a The University of Chicago. $3 1017389
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790 1 0 $a May, Peter, $e advisor
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791 $a Ph.D.
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