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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Remarks on Chern-Simons theory
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by Daniel S. Freed PDF
Bull. Amer. Math. Soc. 46 (2009), 221-254 Request permission


The classical Chern-Simons invariant is the basis for a $3$-dimensional topological quantum field theory. We describe some of the mathematical structure which has been built around this and other topological field theories. We include, in the introduction and the last section, some general discussion about the current interaction between geometry and quantum theories of fields and gravity.
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Additional Information
  • Daniel S. Freed
  • Affiliation: Department of Mathematics, University of Texas, 1 University Station C1200, Austin, Texas 78712-0257
  • Email:
  • Received by editor(s): August 8, 2008
  • Published electronically: January 15, 2009
  • Additional Notes: The author is supported by NSF grant DMS-0603964
    Based on a talk given in the Simons Auditorium in Chern Hall at the Mathematical Sciences Research Institute on the occasion of its $25^{\text {th}}$ Anniversary.

  • Dedicated: Dedicated to MSRI on its $25^{\text {th}}$ anniversary
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 46 (2009), 221-254
  • MSC (2000): Primary 81T45, 53C05, 55N15, 18F99
  • DOI:
  • MathSciNet review: 2476413