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July 2015 Naturality in sutured monopole and instanton homology
John A. Baldwin, Steven Sivek
J. Differential Geom. 100(3): 395-480 (July 2015). DOI: 10.4310/jdg/1432842360

Abstract

In “Knots, sutures, and excision” (J. Differential Geom. 84, 301–364), Kronheimer and Mrowka defined invariants of balanced sutured manifolds using monopole and instanton Floer homology. Their invariants assign isomorphism classes of modules to balanced sutured manifolds. In this paper, we introduce refinements of these invariants which assign much richer algebraic objects called projectively transitive systems of modules to balanced sutured manifolds and isomorphisms of such systems to diffeomorphisms of balanced sutured manifolds. Our work provides the foundation for extending these sutured Floer theories to other interesting functorial frameworks as well, and can be used to construct new invariants of contact structures and (perhaps) of knots and bordered 3-manifolds.

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John A. Baldwin. Steven Sivek. "Naturality in sutured monopole and instanton homology." J. Differential Geom. 100 (3) 395 - 480, July 2015. https://doi.org/10.4310/jdg/1432842360

Information

Published: July 2015
First available in Project Euclid: 28 May 2015

zbMATH: 1334.57008
MathSciNet: MR3352794
Digital Object Identifier: 10.4310/jdg/1432842360

Rights: Copyright © 2015 Lehigh University

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Vol.100 • No. 3 • July 2015
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