Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Toward the group completion of the Burau representation
HTML articles powered by AMS MathViewer

by Jack Morava and Dale Rolfsen HTML | PDF
Trans. Amer. Math. Soc. 376 (2023), 1845-1865 Request permission


Following Boardman-Vogt, McDuff, Segal, and others, we construct a monoidal topological groupoid or space of finite subsets of the plane, and interpret the Burau representation of knot theory as a topological quantum field theory defined on it. Its determinant or writhe is an invertible braided monoidal TQFT which group completes to define a Hopkins-Mahowald model for integral homology as an $E_2$ Thom spectrum. We use these ideas to construct an infinite cyclic (Alexander) cover for the space of finite subsets of $\mathbb {C}$, and we argue that the TQFT defined by Burau is closely related to the SU(2)-valued Wess-Zumino-Witten model for string theory on $\mathbb {R}^3_+$.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2020): 55U40, 20F36
  • Retrieve articles in all journals with MSC (2020): 55U40, 20F36
Additional Information
  • Jack Morava
  • Affiliation: Department of Mathematics, The Johns Hopkins University, Baltimore, Maryland 21218
  • MR Author ID: 217965
  • Email:
  • Dale Rolfsen
  • Affiliation: Pacific Institute for the Mathematical Sciences and Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
  • Email:
  • Received by editor(s): July 30, 2019
  • Received by editor(s) in revised form: April 12, 2022, July 14, 2022, and August 9, 2022
  • Published electronically: November 16, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 1845-1865
  • MSC (2020): Primary 55U40; Secondary 20F36
  • DOI:
  • MathSciNet review: 4549693