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Naturality in sutured monopole and instanton homology

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Title: Naturality in sutured monopole and instanton homology
Authors: Baldwin, JA
Sivek, S
Item Type: Journal Article
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.
Issue Date: 28-May-2015
Date of Acceptance: 1-May-2015
URI: http://hdl.handle.net/10044/1/52051
DOI: https://dx.doi.org/10.4310/jdg/1432842360
ISSN: 0022-040X
Publisher: Project Euclid
Start Page: 395
End Page: 480
Journal / Book Title: Journal of Differential Geometry
Volume: 100
Issue: 3
Copyright Statement: © 2015 Project Euclid
Keywords: math.GT
math.SG
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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