Manifolds and

Cover -- Title page -- Contents -- Preface -- Manifolds, K-theory and the calculus of functors -- 1. Background -- 2. Functors whose derivatives are a module over the Koszul dual of the little discs operad -- 3. A category of pointed framed manifolds -- 4. The Taylor tower of Waldhausen's algebraic K-theory of spaces functor -- Acknowledgements -- References -- Diagrams encoding group actions on Γ-spaces -- 1. Introduction -- 2. Background -- 3. Actions of a fixed group on Γ-spaces -- 4. Varying group actions on Γ-spaces -- Acknowledgement -- References -- Contractible manifolds with exotic positive scalar curvature behavior -- 1. Introduction -- 2. Background -- 3. Contractible -- References -- Relative Schur multipliers and universal extensions of group homomorphisms -- 1. Introduction -- 2. Central -extensions and relative Schur multiplier -- 3. Universal factorizations -- Acknowledgment -- References -- Scissors congruence with mixed dimensions -- Introduction -- 1. The polytope group of a PL space -- 2. Cones -- 3. The ⋆-product -- 4. Relation with McMullen's work -- 5. The local Euler invariant and the ⋆-product -- 6. Euclidean invariants -- 7. The graded rings and -- 8. Manifolds without boundary and Euclidean invariants -- References -- On the moduli space of _{∞}-structures -- 1. Introduction -- 2. Preliminaries -- 3. Proof of Theorem A and Addendum B -- 4. Proof of Theorem E -- 5. Proof of Theorem C -- 6. The augmented case -- 7. Examples -- Acknowledgements -- References -- Nilpotence in the symplectic bordism ring -- References -- A geometric homology representative in the space of knots -- 1. Introduction -- 2. Definition of the cycle -- 3. The Longoni cocycle -- 4. Nontriviality -- 5. Future work -- Appendix A. Isotopies -- References -- Brauer spaces for commutative rings and structured ring spectra -- Introduction.

1. Background on algebraic K-theory -- 2. Whitehead groups and Whitehead spaces -- 3. Brauer spectra for commutative rings -- 4. A scholion on the Azumaya complex -- 5. Brauer spectra for structured ring spectra -- 6. Functoriality -- References -- Bridgeland stability, 2-Segal spaces, and the Ran space of the line -- 1. Introduction -- 2. Bridgeland stability conditions for stable ∞-categories -- 3. Hall-type invariants for stable ∞-categories -- 4. The Hall-type objects associated to stability conditions -- 5. Appendix: Stable ∞-categories -- Acknowledgments -- References -- Occupants in manifolds -- 1. Occupants in a submanifold -- 2. Occupants in the interior of a manifold -- 3. Gates -- 4. Occupants near the gate -- References -- Back Cover.

This volume contains the proceedings of the conference on Manifolds, K-Theory, and Related Topics, held from June 23-27, 2014, in Dubrovnik, Croatia. The articles contained in this volume are a collection of research papers featuring recent advances in homotopy theory, K-theory, and their applications to manifolds. Topics covered include homotopy and manifold calculus, structured spectra, and their applications to group theory and the geometry of manifolds. This volume is a tribute to the influence of Tom Goodwillie in these fields.

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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.