Remarks on Chern-Simons Theory - Mathematics > Algebraic TopologyReport as inadecuate

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Abstract: In the late 1980s Witten used the Chern-Simons form of a connection toconstruct new invariants of 3-manifolds and knots, recovering in particular theJones invariants. Since then the associated topological quantum field theoryTQFT has served as a key example in understanding the structure of TQFTs ingeneral. We survey some of that structure with a particular focus on the-multi-tier- aspects. We discuss general axioms, generators-and-relationstheorems, a priori constructions, dimensional reduction and K-theory, andChern-Simons as a 0-1-2-3 theory. An appendix gives a lightening treatment ofthe Chern-Simons-Weil theory of connections. The paper concludes with generalremarks about the Geometry-QFT-Strings interaction.

Author: Daniel S. Freed


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