Journal of Differential Geometry

Naturality in sutured monopole and instanton homology

John A. Baldwin and Steven Sivek

Full-text: Open access


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

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

First available in Project Euclid: 28 May 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


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.

Export citation