This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields.

A modern compact introduction to factorization homology suited for graduate students Assumes no familiarity with advanced homotopy theory Provides exercises that build intuition and help the reader to learn quickly

Autorentext

Hiro Lee Tanaka is an Assistant Professor at Texas State University. Tanaka's research with collaborators helped lay the foundations for the field of factorization homology. His current research involves applying infinity-categorical techniques to questions in symplectic geometry and mirror symmetry

Lukas Müller obtained his PhD in mathematical physics from Heriot-Watt University Edinburgh in 2020 and is a postdoctoral fellow at the Max-Planck-Institute for Mathematics in Bonn until 2022. His work lies mainly at the intersection of higher category theory, geometry and quantum field theory. He is also interested in quantum topology.

Araminta Amabel is a PhD candidate at MIT, currently studying geometric topology through the lens of factorization homology.

Artem Kalmykov is a PhD student at the Institute of Mathematics, University of Zurich. He obtained his bachelor's degree at Higher School of Economics, Moscow, and Masterof Science at the University of Geneva. His research is mainly concerned with applications of the methods of derived algebraic geometry to representation theory, for instance, to the theory of quantum groups and elliptic algebras.

Zusammenfassung

"The reader with no prior knowledge of the subjects in the title of the book will ... have an idea of topological field theory, an appreciation of the utility of -categories, and the ability to articulate the definition of the new and exciting factorization homology theory. ... A more experienced reader is likely to quite enjoy the ride that ties together various classical notions through one single Kan extension." (Ittay Weiss, MAA Reviews, May 9, 2021)

Inhalt
The one-dimensional case.- Factorization homology in higher dimensions.- Topological field theories and the cobordism hypothesis.