منیفولدها و نظریه K: کنفرانس منیفولدها، نظریه K و موضوعات مرتبط، ۲۳-۲۷ ژوئن ۲۰۱۴، دوبرونیک، کرواسی

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. Cover 1 Title page 4 Contents 8 Preface 10 Manifolds, K-theory and the calculus of functors 12 1. Background 14 2. Functors whose derivatives are a module over the Koszul dual of the little discs operad 17 3. A category of pointed framed manifolds 27 4. The Taylor tower of Waldhausen’s algebraic K-theory of spaces functor 37 Acknowledgements 47 References 47 Diagrams encoding group actions on Γ-spaces 50 1. Introduction 50 2. Background 51 3. Actions of a fixed group on Γ-spaces 53 4. Varying group actions on Γ-spaces 56 Acknowledgement 60 References 61 Contractible manifolds with exotic positive scalar curvature behavior 62 1. Introduction 62 2. Background 63 3. Contractible 65 References 74 Relative Schur multipliers and universal extensions of group homomorphisms 76 1. Introduction 76 2. Central f-extensions and relative Schur multiplier 79 3. Universal factorizations 89 Acknowledgment 91 References 91 Scissors congruence with mixed dimensions 92 Introduction 92 1. The polytope group of a PL space 96 2. Cones 108 3. The ⋆-product 116 4. Relation with McMullen’s work 123 5. The local Euler invariant and the ⋆-product 127 6. Euclidean invariants 128 7. The graded rings E and L 136 8. Manifolds without boundary and Euclidean invariants 144 References 150 On the moduli space of A_{∞}-structures 152 1. Introduction 152 2. Preliminaries 157 3. Proof of Theorem A and Addendum B 159 4. Proof of Theorem E 162 5. Proof of Theorem C 165 6. The augmented case 166 7. Examples 167 Acknowledgements 168 References 169 Nilpotence in the symplectic bordism ring 172 References 176 A geometric homology representative in the space of knots 178 1. Introduction 178 2. Definition of the cycle 179 3. The Longoni cocycle 186 4. Nontriviality 189 5. Future work 194 Appendix A. Isotopies 196 References 198 Brauer spaces for commutative rings and structured ring spectra 200 Introduction 200 1. Background on algebraic K-theory 202 2. Whitehead groups and Whitehead spaces 204 3. Brauer spectra for commutative rings 206 4. A scholion on the Azumaya complex 210 5. Brauer spectra for structured ring spectra 212 6. Functoriality 215 References 217 Bridgeland stability, 2-Segal spaces, and the Ran space of the line 220 1. Introduction 220 2. Bridgeland stability conditions for stable ∞-categories 222 3. Hall-type invariants for stable ∞-categories 233 4. The Hall-type objects associated to stability conditions 239 5. Appendix: Stable ∞-categories 241 Acknowledgments 245 References 246 Occupants in manifolds 248 1. Occupants in a submanifold 248 2. Occupants in the interior of a manifold 258 3. Gates 262 4. Occupants near the gate 267 References 270 Back Cover 274 Contains the proceedings of the conference on Manifolds, $K$-Theory, and Related Topics, held in June, 2014. The articles 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.