Transgression is a relationship between higher-categorical geometry on a manifold M and infinite-dimensional geometry on the loop space LM. This mutual connection is highly insightful for both domains, as distinct insights are known on each side, and the acquired knowledge can be transferred reciprocally.
Transgression serves as a fundamental method in string geometry, and more broadly in the study of smooth functorial field theories. A multiplicative version of transgression explores extensions of loop groups and their connection to extensions of higher-categorical groups.
Below are some articles and manuscripts of talks about this topic.
Articles associated with this topic
String structures and loop spaces
Encyclopedia of Mathematical Physics (2nd edition), to appear
arxiv:2312.12998The stringor bundle
arxiv:2206.09797Smooth Functorial Field Theories from B-Fields and D-Branes
together with Severin Bunk
J. Homotopy Relat. Struct. 16.1 (2021): 75-153
arxiv:1911.09990Transgression of D-branes
together with Severin Bunk
Adv. Theor. Math. Phys., Vol. 25, No. 5 (2021), pp. 1095-1198.
arxiv:1808.04894Transgressive loop group extensions
Math. Z. 286(1) 325-360, 2017
arxiv:1502.05089A Construction of String 2-Group Models using a Transgression-Regression Technique
Analysis, Geometry and Quantum Field Theory, edited by C. L. Aldana, M. Braverman, B. Iochum, and C. Neira-Jiménez, volume 584 of Contemp. Math., pages 99-115, AMS, 2012
arxiv:1201.5052Lifting Problems and Transgression for Non-Abelian Gerbes
together with Thomas Nikolaus
Adv. Math. 242 (2013) 50-79
arxiv:1112.4702Transgression to Loop Spaces and its Inverse, III: Gerbes and Thin Fusion Bundles
Adv. Math. 231 (2012), 3445-3472
arxiv:1109.0480A Loop Space Formulation for Geometric Lifting Problems
J. Aust. Math. Soc. 90, 129-144 (2011)
arxiv:1007.5373Transgression to Loop Spaces and its Inverse, II: Gerbes and Fusion Bundles with Connection
Asian J. Math., Vol. 20, No. 1 (2016), pp. 59-116
arxiv:1004.0031Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps
Cah. Topol. Géom. Différ. Catég., 2012, Vol. LIII, 162-210
arxiv:0911.3212Multiplicative Bundle Gerbes with Connection
Differential Geom. Appl. 28(3), 313-340 (2010)
arxiv:0804.4835
Talks associated with this topic
Transgression of Gerbes to Loop Spaces
Workshop "Higher Structures in Topology and Geometry IV", Georg-August-Universität Göttingen, June 2010
NotesAbelian gauge theories on loop spaces and their regression
Workshop "Higher Gauge Theory, TQFT and Quantum Gravity", Instituto Superior Técnico Lisboa, February 2011
NotesA loop space formulation for the geometry of abelian gerbes
Conference "Analysis, Geometry, and Quantum Field Theory", Universität Potsdam, October 2011
NotesDifferential string classes and loop spaces
Workshop "Differential Cohomologies", The Graduate Center, CUNY, August 2014
Video NotesString structures and supersymmetric sigma models
Program "Higher structures in string theory and quantum field theory", Erwin-Schrödinger-Institut für Mathematische Physik, December 2015
NotesTransgressive central extensions of loop groups
Conference "Colloquium on Algebras and Representations - Quantum 2016", Universidad Nacional de Córdoba, March 2016
NotesString geometry and spin geometry on loop spaces
Parallel session "Mathematical aspects of string theory and string geometry", Friedrich-Schiller-Universität Jena, July 2016
NotesString connections and loop spaces
Workshop "Loop spaces, supersymmetry and index theory", Nankai University at Tianjin, July 2017
PresentationFusion in loop spaces
Workshop "Geometric Quantization", Banff International Research Station for Mathematical Innovation and Discovery, April 2018
VideoTransgression of higher structures to loop spaces
Workshop "Loop Space and Higher Category", online, December 2022
PresentationThe stringor bundle
Conference "Geometries from Strings and Fields", Galileo Galilei Institute, July 2023
Video