Journal of Differential Geometry

Naturality in sutured monopole and instanton homology

John A. Baldwin and Steven Sivek

Full-text: Open access

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.

Article information

Source
J. Differential Geom., Volume 100, Number 3 (2015), 395-480.

Dates
First available in Project Euclid: 28 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1432842360

Digital Object Identifier
doi:10.4310/jdg/1432842360

Mathematical Reviews number (MathSciNet)
MR3352794

Zentralblatt MATH identifier
1334.57008

Citation

Baldwin, John A.; Sivek, Steven. Naturality in sutured monopole and instanton homology. J. Differential Geom. 100 (2015), no. 3, 395--480. doi:10.4310/jdg/1432842360. https://projecteuclid.org/euclid.jdg/1432842360


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