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Introductory lectures on topological quantum field theory

Volume 114 / 2018

Nils Carqueville, Ingo Runkel Banach Center Publications 114 (2018), 9-47 MSC: 18D05, 57R56. DOI: 10.4064/bc114-1


These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the definition in terms symmetric monoidal categories, and we highlight the algebraic formulation emerging from a formal generators-and-relations description. This allows one to understand (oriented, closed) 1- and 2-dimensional TQFTs in terms of a finite amount of algebraic data, while already the 3-dimensional case needs an infinite amount of data. We evade these complications by instead discussing some aspects of 3-dimensional extended TQFTs, and their relation to braided monoidal categories.


  • Nils CarquevilleFakultät für Mathematik
    Universität Wien
  • Ingo RunkelFachbereich Mathematik
    Universität Hamburg

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