%0 Journal Article %1 carqueville2017introductory %A Carqueville, Nils %A Runkel, Ingo %D 2017 %K qft review topology %T Introductory lectures on topological quantum field theory %U http://arxiv.org/abs/1705.05734 %X 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.

@article{carqueville2017introductory, abstract = {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.}, added-at = {2017-05-27T16:20:12.000+0200}, author = {Carqueville, Nils and Runkel, Ingo}, biburl = {https://www.bibsonomy.org/bibtex/23a7b76f1fa9215f083b9171dd6df2f02/vindex10}, description = {Introductory lectures on topological quantum field theory}, interhash = {e06e5a0a92d62f11a7d779ec36c031e9}, intrahash = {3a7b76f1fa9215f083b9171dd6df2f02}, keywords = {qft review topology}, note = {cite arxiv:1705.05734Comment: 48 pages}, timestamp = {2017-05-27T16:20:12.000+0200}, title = {Introductory lectures on topological quantum field theory}, url = {http://arxiv.org/abs/1705.05734}, year = 2017 }