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2021 No homotopy 4–sphere invariants using ECH=SWF
Chris Gerig
Algebr. Geom. Topol. 21(5): 2543-2569 (2021). DOI: 10.2140/agt.2021.21.2543

Abstract

In relation to the 4–dimensional smooth Poincaré conjecture, we construct a tentative invariant of homotopy 4–spheres using embedded contact homology (ECH) and Seiberg–Witten theory (SWF). But, for good reason, it is a constant value independent of the sphere, so this null result demonstrates that one should not try to use the usual theories of ECH and SWF. On the other hand, a corollary is that there always exist pseudoholomorphic curves satisfying certain constraints in (punctured) 4–spheres.

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Chris Gerig. "No homotopy 4–sphere invariants using ECH=SWF." Algebr. Geom. Topol. 21 (5) 2543 - 2569, 2021. https://doi.org/10.2140/agt.2021.21.2543

Information

Received: 13 April 2020; Revised: 11 October 2020; Accepted: 27 October 2020; Published: 2021
First available in Project Euclid: 29 November 2021

Digital Object Identifier: 10.2140/agt.2021.21.2543

Subjects:
Primary: 53D42
Secondary: 57K41

Keywords: 4–sphere , ECH , Gromov , near-symplectic , Seiberg–Witten

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 5 • 2021
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