Geometry of Loop Spaces and the Cobar Construction.

Intro -- Contents -- Introduction -- Prologue -- Chapter I: The bar and cobar constructions -- 1 The geometric bar construction -- 2 The geometric cobar construction for simplicial spaces -- 3 The algebraic bar and cobar constructions -- Appendix 1: The cobar construction of Adams -- Appendix 2: Loop spaces of projective spaces -- 4 Adjunction and strongly homotopy multiplicative maps -- Chapter II: A model theorem for loop spaces -- 1 Realization of functors -- Appendix: DI categories with retractions -- 2 A model theorem for loop spaces -- 3 Approximation of path spaces -- 4 Proof of the model theorem -- Chapter III: On the desuspension of model functors -- 1 Abstract complexes -- 2 Model functors and their desuspension by cellular strings -- Appendix: Reduced model functors and iterated loop spaces -- 3 Cellular strings in the simplex -- 4 Cellular strings in the cube -- 5 Simplicial subdivision of cubes and cubical subdivision of parallelohedra -- 6 Cellular strings in products of simplices -- 7 Cellular strings in the parallelohedron C[sup(n)] -- Chapter IV: Applications -- 1 The geometric cobar construction -- 2 A diagonal for the cobar construction and a model for the double loop space of a simplicial space -- 3 CW-models of Milgram for Ω[sup(n)]Σ[sup(n)]× -- Appendix: The cellular chain complex of the Milgram models -- 4 A CW-model for Ω[sup(n)]S[sup(n)] -- 5 A model for ΩΩ[sup(n)]Σ[sup(n)]× -- Appendix: On the suspension of Hopf maps -- References -- Index -- A -- B -- C -- D -- E -- F -- H -- I -- J -- K -- L -- M -- O -- P -- R -- S -- T -- V -- W.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.