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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 .

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On the intersection ring of graph manifolds
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by Margaret I. Doig and Peter D. Horn PDF
Trans. Amer. Math. Soc. 369 (2017), 1185-1203 Request permission

Abstract:

We calculate the intersection ring of 3-dimensional graph manifolds with rational coefficients and give an algebraic characterization of these rings when the manifold’s underlying graph is a tree. We are able to use this characterization to show that the intersection ring obstructs arbitrary 3-manifolds from being homology cobordant to certain graph manifolds.
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Additional Information
  • Margaret I. Doig
  • Affiliation: Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, New York 13244-1150
  • MR Author ID: 1076165
  • Email: midoig@syr.edu
  • Peter D. Horn
  • Affiliation: Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, New York 13244-1150
  • MR Author ID: 855878
  • Email: pdhorn@syr.edu
  • Received by editor(s): January 9, 2015
  • Received by editor(s) in revised form: March 20, 2015
  • Published electronically: March 1, 2016
  • Additional Notes: The second author was partially supported by National Science Foundation DMS-1258630
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1185-1203
  • MSC (2010): Primary 57M27
  • DOI: https://doi.org/10.1090/tran/6722
  • MathSciNet review: 3572270