Pin(2)-Equivariant Seiberg-Witten Floer homology and the Triangulation Conjecture
Author:
Ciprian Manolescu
Journal:
J. Amer. Math. Soc. 29 (2016), 147-176
MSC (2010):
Primary 57R58; Secondary 57Q15, 57M27
DOI:
https://doi.org/10.1090/jams829
Published electronically:
April 22, 2015
MathSciNet review:
3402697
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We define -equivariant Seiberg-Witten Floer homology for rational homology
-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
reduction is the Rokhlin invariant. As an application, we show that there are no homology
-spheres
of the Rokhlin invariant one such that
bounds an acyclic smooth
-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
Email:
cm@math.ucla.edu
DOI:
https://doi.org/10.1090/jams829
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.
Article copyright:
© Copyright 2015
American Mathematical Society