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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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Degeneracy loci of families of Dirac operators
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by Thomas G. Leness PDF
Trans. Amer. Math. Soc. 364 (2012), 5995-6008 Request permission


Generalizing some results from R. Leung’s thesis, we compute, in rational cohomology, the Poincaré dual of the degeneracy locus of the family of Dirac operators parameterized by the moduli space of projectively anti-self-dual $\operatorname {SO}(3)$ connections on a closed four-manifold. This should be a useful tool in comparing gauge theoretic invariants of smooth four-manifolds.
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Additional Information
  • Thomas G. Leness
  • Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
  • Email:
  • Received by editor(s): November 23, 2009
  • Received by editor(s) in revised form: March 4, 2011
  • Published electronically: June 12, 2012
  • Additional Notes: The author was supported in part by a Florida International University Faculty Research Grant and by NSF grant DMS #0905786.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 5995-6008
  • MSC (2010): Primary 53C07, 57R57, 58J05, 58J20, 58J52
  • DOI:
  • MathSciNet review: 2946940