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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Pin(2)-Equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
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by Ciprian Manolescu PDF
J. Amer. Math. Soc. 29 (2016), 147-176 Request permission


We define $\operatorname {Pin}(2)$-equivariant Seiberg-Witten Floer homology for rational homology $3$-spheres equipped with a spin structure. The analogue of Frøyshov’s correction term in this setting is an integer-valued invariant of homology cobordism whose mod $2$ reduction is the Rokhlin invariant. As an application, we show that there are no homology $3$-spheres $Y$ of the Rokhlin invariant one such that $Y \#Y$ bounds an acyclic smooth $4$-manifold. By previous work of Galewski-Stern and Matumoto, this implies the existence of non-triangulable high-dimensional manifolds.
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Additional Information
  • Ciprian Manolescu
  • Affiliation: Department of Mathematics, UCLA, 520 Portola Plaza, Los Angeles, California 90095
  • MR Author ID: 677111
  • Email:
  • Received by editor(s): April 10, 2013
  • Received by editor(s) in revised form: February 6, 2014, September 17, 2014, and October 6, 2014
  • Published electronically: April 22, 2015
  • Additional Notes: The author was supported by NSF grant DMS-1104406.
  • © Copyright 2015 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 29 (2016), 147-176
  • MSC (2010): Primary 57R58; Secondary 57Q15, 57M27
  • DOI:
  • MathSciNet review: 3402697