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On the intersection ring of graph manifolds


Authors: Margaret I. Doig and Peter D. Horn
Journal: Trans. Amer. Math. Soc. 369 (2017), 1185-1203
MSC (2010): Primary 57M27
DOI: https://doi.org/10.1090/tran/6722
Published electronically: March 1, 2016
MathSciNet review: 3572270
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Abstract | References | Similar Articles | Additional Information

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
Email: midoig@syr.edu

Peter D. Horn
Affiliation: Department of Mathematics, Syracuse University, 215 Carnegie Building, Syracuse, New York 13244-1150
Email: pdhorn@syr.edu

DOI: https://doi.org/10.1090/tran/6722
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
Article copyright: © Copyright 2016 American Mathematical Society

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