Women in Topology : Collaborations in Homotopy Theory.
Basterra, Maria.
Women in Topology : Collaborations in Homotopy Theory. - 1st ed. - 1 online resource (178 pages) - Contemporary Mathematics ; v.641 . - Contemporary Mathematics .
Cover -- Title page -- Contents -- Preface -- Representations of Derived -infinity Algebras -- Acknowledgements -- 1. Introduction -- 2. Review of derived _-algebras -- 3. Coalgebras over the Koszul dual cooperad -- 4. Representations of derived _-algebras -- 5. New example of a derived _-algebra -- 6. Appendix: sign conventions -- References -- Unbased Calculus for Functors to Chain Complexes -- 1. Introduction -- 2. Unbased Cotriple Calculus -- 3. Iterated fibers in (ℛ) -- 4. The Cotriple -- References -- Left-Induced Model Structures and Diagram Categories -- 1. Introduction -- 1.1. Acknowledgements -- 2. Left-induced model structures -- 2.1. Fibrant generation and Postnikov presentations of model categories -- 2.2. Existence of left-induced model structures -- 2.3. Elementary properties of left-induced structures -- 3. Examples -- 3.1. An explicit Postnikov presentation -- 3.2. An application of Theorem 2.23 -- 4. Injective model structures -- 4.1. Diagrams as algebras -- 4.2. Diagrams as coalgebras -- 4.3. Existence of injective model structures -- 4.4. Properties of injective model structures -- 5. (Generalized) Reedy diagram categories and fibrant generation -- 5.1. The case of Reedy categories -- 5.2. The case of generalized Reedy categories -- Appendix A. Enriched model categories -- A.1. Enriched categories, functors, adjunctions -- A.2. Enriched diagram categories -- References -- Fixed Points of -Toral Groups Acting on Partition Complexes -- 1. Introduction -- 2. Homotopy type of \Lcal_ for small -- 3. Group-theoretic results -- 4. Conditions for contractibility of the fixed point sets -- 5. Proof of the main theorem -- 6. Examples -- References -- On the Higher Topological Hochschild Homology of _ and Commutative _-Group Algebras -- 1. Introduction. 2. Comparing the bar construction and its homology for some basic algebras -- 3. Veen's spectral sequence and iterated Tors -- 4. Pushing Veen's bounds -- 5. \THH^(\F₂), up to =3 and a stable element -- 6. A splitting of \THH^( [ ]) for abelian groups -- 7. The higher Bökstedt spectral sequence -- 8. Higher Hochschild homology of (truncated) polynomial algebras -- 9. Étale and Galois descent -- 10. Group algebras of finitely generated abelian groups -- Appendix A. Code -- References -- A Model Structure on -- Introduction -- 1. Model structures on -categories -- 2. The model category \gcat -- 3. Cellular functors and left proper model structures -- References -- Orbispaces and Their Mapping Spaces via Groupoids: A Categorical Approach -- 1. Introduction -- 2. Topological Groupoids and Orbigroupoids -- 3. Homomorphisms and Natural Transformations of Orbigroupoids -- 4. Representing Orbispaces with Orbigroupoids -- 5. Mapping Spaces for Orbigroupoids: Defining \GMap(\calG,\calH) -- 6. Inertia Groupoids and Mapping Groupoids -- 7. Conclusion -- References -- Back Cover.
This volume contains the proceedings of the WIT: Women in Topology workshop, held from August 18-23, 2013, at the Banff International Research Station, Banff, Alberta, Canada. The Women in Topology workshop was devoted primarily to active collaboration by teams of five to seven participants, each including senior and junior researchers, as well as graduate students. This volume contains papers based on the results obtained by team projects in homotopy theory, including A-infinity structures, equivariant homotopy theory, functor calculus, model categories, orbispaces, and topological Hochschild homology.
9781470424954
Homotopy theory--Congresses.
Electronic books.
QA612.7.W664 2015
514/.2409252
Women in Topology : Collaborations in Homotopy Theory. - 1st ed. - 1 online resource (178 pages) - Contemporary Mathematics ; v.641 . - Contemporary Mathematics .
Cover -- Title page -- Contents -- Preface -- Representations of Derived -infinity Algebras -- Acknowledgements -- 1. Introduction -- 2. Review of derived _-algebras -- 3. Coalgebras over the Koszul dual cooperad -- 4. Representations of derived _-algebras -- 5. New example of a derived _-algebra -- 6. Appendix: sign conventions -- References -- Unbased Calculus for Functors to Chain Complexes -- 1. Introduction -- 2. Unbased Cotriple Calculus -- 3. Iterated fibers in (ℛ) -- 4. The Cotriple -- References -- Left-Induced Model Structures and Diagram Categories -- 1. Introduction -- 1.1. Acknowledgements -- 2. Left-induced model structures -- 2.1. Fibrant generation and Postnikov presentations of model categories -- 2.2. Existence of left-induced model structures -- 2.3. Elementary properties of left-induced structures -- 3. Examples -- 3.1. An explicit Postnikov presentation -- 3.2. An application of Theorem 2.23 -- 4. Injective model structures -- 4.1. Diagrams as algebras -- 4.2. Diagrams as coalgebras -- 4.3. Existence of injective model structures -- 4.4. Properties of injective model structures -- 5. (Generalized) Reedy diagram categories and fibrant generation -- 5.1. The case of Reedy categories -- 5.2. The case of generalized Reedy categories -- Appendix A. Enriched model categories -- A.1. Enriched categories, functors, adjunctions -- A.2. Enriched diagram categories -- References -- Fixed Points of -Toral Groups Acting on Partition Complexes -- 1. Introduction -- 2. Homotopy type of \Lcal_ for small -- 3. Group-theoretic results -- 4. Conditions for contractibility of the fixed point sets -- 5. Proof of the main theorem -- 6. Examples -- References -- On the Higher Topological Hochschild Homology of _ and Commutative _-Group Algebras -- 1. Introduction. 2. Comparing the bar construction and its homology for some basic algebras -- 3. Veen's spectral sequence and iterated Tors -- 4. Pushing Veen's bounds -- 5. \THH^(\F₂), up to =3 and a stable element -- 6. A splitting of \THH^( [ ]) for abelian groups -- 7. The higher Bökstedt spectral sequence -- 8. Higher Hochschild homology of (truncated) polynomial algebras -- 9. Étale and Galois descent -- 10. Group algebras of finitely generated abelian groups -- Appendix A. Code -- References -- A Model Structure on -- Introduction -- 1. Model structures on -categories -- 2. The model category \gcat -- 3. Cellular functors and left proper model structures -- References -- Orbispaces and Their Mapping Spaces via Groupoids: A Categorical Approach -- 1. Introduction -- 2. Topological Groupoids and Orbigroupoids -- 3. Homomorphisms and Natural Transformations of Orbigroupoids -- 4. Representing Orbispaces with Orbigroupoids -- 5. Mapping Spaces for Orbigroupoids: Defining \GMap(\calG,\calH) -- 6. Inertia Groupoids and Mapping Groupoids -- 7. Conclusion -- References -- Back Cover.
This volume contains the proceedings of the WIT: Women in Topology workshop, held from August 18-23, 2013, at the Banff International Research Station, Banff, Alberta, Canada. The Women in Topology workshop was devoted primarily to active collaboration by teams of five to seven participants, each including senior and junior researchers, as well as graduate students. This volume contains papers based on the results obtained by team projects in homotopy theory, including A-infinity structures, equivariant homotopy theory, functor calculus, model categories, orbispaces, and topological Hochschild homology.
9781470424954
Homotopy theory--Congresses.
Electronic books.
QA612.7.W664 2015
514/.2409252