Higher structures in topology, geometry, and physics

• Titel: Higher structures in topology, geometry, and physics
• Mitwirkende: Kaufmann, Ralph M. [HerausgeberIn]
• Mitwirkende: Markl, Martin [HerausgeberIn]
• Mitwirkende: Voronov, Alexander A. [HerausgeberIn]
• Körperschaft: AMS Special Session Higher Structures in Topology, Geometry, and Physics <Online, 2022> [VerfasserIn]
• Verf.angabe: Ralph M. Kaufmann, Martin Markl, Alexander A. Voronov, editors
• Verlagsort: Providence, Rhode Island
• Verlag: American Mathematical Society
• Jahr: 2024
• Umfang: 1 Online-Ressource (vii, 321 Seiten)
• Gesamttitel/Reihe: Contemporary mathematics ; 802
• Fussnoten: Description based on publisher supplied metadata and other sources ; "AMS Special Session, Higher Structures in Topology, Geometry and Physics, Virtual March 26-27, 2022."
• ISBN: 978-1-4704-7642-7
• Schlagwörter: (s)Mehrpunktfunktion / (s)Operade / (s)Homotopietheorie / (s)Hochschild-Homologie / (s)Stringtheorie / (s)Topologische Quantenfeldtheorie / (s)Struktur <Mathematik>
• Datenträger: Online-Ressource
• Dokumenttyp: Konferenzschrift
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Higher structures in topology, geometry and physics. - Providence, Rhode Island : American Mathematical Society, 2024. - pages cm
• Sach-SW: Algebraic topology -- Homology and cohomology theories
• Sach-SW: Quantum theory -- Quantum field theory; related classical field theories
• Sach-SW: Associative rings and algebras -- Hopf algebras, quantum groups and related topics
• Sach-SW: Several complex variables and analytic spaces -- Deformations of analytic structures
• Sach-SW: Manifolds and cell complexes -- PL-topology
• K10plus-PPN: 1897530188
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

This volume contains the proceedings of the AMS Special Session on Higher Structures in Topology, Geometry, and Physics, held virtually on March 26-27, 2022. The articles give a snapshot survey of the current topics surrounding the mathematical formulation of field theories. There is an intricate interplay between geometry, topology, and algebra which captures these theories. The hallmark are higher structures, which one can consider as the secondary algebraic or geometric background on which the theories are formulated. The higher structures considered in the volume are generalizations of operads, models for conformal field theories, string topology, open/closed field theories, BF/BV formalism, actions on Hochschild complexes and related complexes, and their geometric and topological aspects.

Abstract

Cover -- Title page -- Contents -- Preface -- On noncommutative differential forms -- 1. Introduction -- 2. Noncommutative forms -- 3. Noncommutative De Rham complex -- 4. The extended noncommutative De Rham complex -- 5. Recollection on cyclic homology -- 6. The extended HKR morphism -- 7. The extended De Rham complex and Hochschild homology -- 8. The ( _{Δ}, ) double complex -- 9. The extended noncommutative De Rham complex and the representation scheme -- 10. Noncommutative Poincaré lemma and the categorical nature of the differentials -- Acknowledgments -- References -- An algebraic model for the free loop space -- 1. Introduction -- 2. Preliminaries -- 3. Categorical coalgebras and the cobar construction -- 4. Chains on a simplicial set and the dg category of paths -- 5. The co-Hochschild complex of a categorical coalgebra -- 6. The co-Hochschild complex as a model for the free loop space -- 7. dg Hopf algebras and the adjoint action -- Acknowledgments -- References -- The structure of simply colored coalgebras -- Introduction -- 1. Preliminaries -- 2. Algebraic perspective -- 3. Categorical perspective -- Acknowledgments -- References -- On examples and classification of Frobenius objects in Rel -- 1. Introduction -- 2. Frobenius objects and TQFT -- 3. Frobenius objects in Rel -- 4. Topological invariants -- 5. The two element case -- 6. The three element case -- 7. Future directions -- Acknowledgments -- References -- Stirling decomposition of graph homology in genus 1 -- 1. Introduction -- 2. Stirling numbers -- 3. Stirling complexes -- 4. Homology of Stirling complexes -- 5. Application to commutative graph homology -- Appendix A. Trees and graphs -- Acknowledgments -- References -- A combinatorial model for the moduli of bordered Riemann surfaces and a compactification -- 1. Introduction -- 2. Polytopes -- 3. Ribbon graphs.