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:2312.12998*The stringor bundle*

arxiv:2206.09797*Smooth Functorial Field Theories from B-Fields and D-Branes*

together with Severin Bunk

J. Homotopy Relat. Struct. 16.1 (2021): 75-153

arxiv:1911.09990*Transgression of D-branes*

together with Severin Bunk

Adv. Theor. Math. Phys., Vol. 25, No. 5 (2021), pp. 1095-1198.

arxiv:1808.04894*Transgressive loop group extensions*

Math. Z. 286(1) 325-360, 2017

arxiv:1502.05089*A 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:1201.5052*Lifting Problems and Transgression for Non-Abelian Gerbes*

together with Thomas Nikolaus

Adv. Math. 242 (2013) 50-79

arxiv:1112.4702*Transgression to Loop Spaces and its Inverse, III: Gerbes and Thin Fusion Bundles*

Adv. Math. 231 (2012), 3445-3472

arxiv:1109.0480*A Loop Space Formulation for Geometric Lifting Problems*

J. Aust. Math. Soc. 90, 129-144 (2011)

arxiv:1007.5373*Transgression 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:1004.0031*Transgression to Loop Spaces and its Inverse, I: Diffeological Bundles and Fusion Maps*

Cah. Topol. Géom. Différ. Catég., 2012, Vol. LIII, 162-210

arxiv:0911.3212*Multiplicative 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

Notes*Abelian gauge theories on loop spaces and their regression*

Workshop "Higher Gauge Theory, TQFT and Quantum Gravity", Instituto Superior Técnico Lisboa, February 2011

Notes*A loop space formulation for the geometry of abelian gerbes*

Conference "Analysis, Geometry, and Quantum Field Theory", Universität Potsdam, October 2011

Notes*Differential string classes and loop spaces*

Workshop "Differential Cohomologies", The Graduate Center, CUNY, August 2014

Video Notes*String structures and supersymmetric sigma models*

Program "Higher structures in string theory and quantum field theory", Erwin-Schrödinger-Institut für Mathematische Physik, December 2015

Notes*Transgressive central extensions of loop groups*

Conference "Colloquium on Algebras and Representations - Quantum 2016", Universidad Nacional de Córdoba, March 2016

Notes*String geometry and spin geometry on loop spaces*

Parallel session "Mathematical aspects of string theory and string geometry", Friedrich-Schiller-Universität Jena, July 2016

Notes*String connections and loop spaces*

Workshop "Loop spaces, supersymmetry and index theory", Nankai University at Tianjin, July 2017

Presentation*Fusion in loop spaces*

Workshop "Geometric Quantization", Banff International Research Station for Mathematical Innovation and Discovery, April 2018

Video*Transgression of higher structures to loop spaces*

Workshop "Loop Space and Higher Category", online, December 2022

Presentation*The stringor bundle*

Conference "Geometries from Strings and Fields", Galileo Galilei Institute, July 2023

Video