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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Conformal cochains
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by Scott O. Wilson PDF
Trans. Amer. Math. Soc. 360 (2008), 5247-5264 Request permission

Addendum: Trans. Amer. Math. Soc. 365 (2013), 5033-5033.

Abstract:

In this paper we define holomorphic cochains and an associated period matrix for triangulated closed topological surfaces. We use the combinatorial Hodge star operator introduced in the author’s paper of 2007, which depends on the choice of an inner product on the simplicial 1-cochains.

We prove that for a triangulated Riemannian 2-manifold (or a Riemann surface), and a particularly nice choice of inner product, the combinatorial period matrix converges to the (conformal) Riemann period matrix as the mesh of the triangulation tends to zero.

References
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Additional Information
  • Scott O. Wilson
  • Affiliation: School of Mathematics, University of Minnesota-Twin Cities, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, Minnesota 55455
  • MR Author ID: 812534
  • Email: scottw@math.umn.edu
  • Received by editor(s): August 8, 2006
  • Published electronically: April 10, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 5247-5264
  • MSC (2000): Primary 57R57, 32G20; Secondary 30F99
  • DOI: https://doi.org/10.1090/S0002-9947-08-04556-X
  • MathSciNet review: 2415073