Geometry of Loop Spaces and the Cobar Construction.
Baues, Hans J.
Geometry of Loop Spaces and the Cobar Construction. - 1st ed. - 1 online resource (194 pages) - Memoirs of the American Mathematical Society ; v.25 . - Memoirs of the American Mathematical Society .
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.
9781470406349
Loop spaces.
Cobar construction (Topology).
Functor theory.
Complexes, Semisimplicial.
Electronic books.
QA612.76 -- .B38 1980eb
510 s;514/.224
Geometry of Loop Spaces and the Cobar Construction. - 1st ed. - 1 online resource (194 pages) - Memoirs of the American Mathematical Society ; v.25 . - Memoirs of the American Mathematical Society .
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.
9781470406349
Loop spaces.
Cobar construction (Topology).
Functor theory.
Complexes, Semisimplicial.
Electronic books.
QA612.76 -- .B38 1980eb
510 s;514/.224