Naturality in sutured monopole and instanton homology

John A. Baldwin; Steven Sivek

doi:10.4310/jdg/1432842360

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arXiv · 1305.4156

Naturality in sutured monopole and instanton homology

John A. Baldwin·Steven Sivek

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Abstract

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. 2013-05-17. Naturality in sutured monopole and instanton homology. https://doi.org/10.4310/jdg%2F1432842360

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