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Homotopy theory for stratified spacesMiller, David January 2010 (has links)
There are many different notions of stratified spaces. This thesis concerns homotopically stratified spaces. These were defined by Frank Quinn in his paper Homotopically Stratified Sets ([16]). His definition of stratified space is very general and relates strata by “homotopy rather than geometric conditions”. This makes homotopically stratified spaces the ideal class of stratified spaces on which to define and study stratified homotopy theory. In the study of stratified spaces it is useful to examine spaces of popaths (paths which travel from lower strata to higher strata) and holinks (those spaces of popaths which immediately leave a lower stratum for their final stratum destination). It is not immediately clear that for adjacent strata these two path spaces are homotopically equivalent and even less clear that this equivalence can be constructed in a useful way. The first aim of this thesis is to prove such an equivalence exists for homotopically stratified spaces. We will define stratified analogues of the usual definitions of maps, homotopies and homotopy equivalences. Then we will provide an elementary criterion for deciding when a strongly stratified map is a stratified homotopy equivalence. This criterion states that a strongly stratified map is a stratified homotopy equivalence if and only if the induced maps on strata and holink spaces are homotopy equivalences. Using this criterion we will prove that any homotopically stratified space is stratified homotopy equivalent to a homotopically stratified space where neighborhoods of strata are mapping cylinders. Finally we will develop categorical descriptions of the class of homotopically stratified spaces up to stratified homotopy. The first of these categorical descriptions will involve categories with a topology on their object and morphism sets. The second categorical description will involve only categories with discrete object spaces.
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The rational homotopy types of configuration spaces of three-dimensional lens spaces /Miller, Matthew Sean, January 2007 (has links)
Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaf 76). Also available for download via the World Wide Web; free to University of Oregon users.
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Primal dual pursuit a homotopy based algorithm for the Dantzig selector /Asif, Muhammad Salman January 2008 (has links)
Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Romberg, Justin; Committee Member: McClellan, James; Committee Member: Mersereau, Russell
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The cohomology of finite subgroups of Morava stabilizer groups and Smith-Toda complexes /Nave, Lee Stewart. January 1999 (has links)
Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (leaves 41-42).
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Enriched sheaf theory as a framework for stable homotopy theory /Johnson, Mark William. January 1999 (has links)
Thesis (Ph. D.)--University of Washington, 1999. / Vita. Includes bibliographical references (leaves 170-171).
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Stabilization of chromatic functors /Leeman, Aaron, January 2009 (has links)
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 33-34) Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.
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A construction of a differential graded Lie algebra in the category of effective homological motives /Gartz, Kaj M. January 2003 (has links)
Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2003. / Includes bibliographical references. Also available on the Internet.
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Triangulating homotopy equivalencesSullivan, Dennis Parnell, January 1900 (has links)
Thesis--Princeton University, 1966. / Includes bibliographical references.
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A model structure on the category of pro-simplicial sets /Isaksen, Daniel C. January 1999 (has links)
Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 1999. / Includes bibliographical references. Also available on the Internet.
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The generating hypothesis in general stable homotopy categories /Lockridge, Keir H. January 2006 (has links)
Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 31-32).
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