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7 papers · 2 filters
The signature of positive braids is linearly bounded by their first Betti number
Peter Feller
We provide linear lower bounds for the signature of positive braids in terms of the three genus of their braid closure. This yields linear bounds for the topological slice genus of…
Identities on Hyperbolic Manifolds
Martin Bridgeman, Ser Peow Tan
In this survey, we discuss four classes of identities due principally to Basmajian, McShane, Bridgeman-Kahn and Luo-Tan on hyperbolic manifolds and provide a unified approach for p…
Non-simple genus minimizers in lens spaces
Joshua Evan Greene, Yi Ni
Given a one-dimensional homology class in a lens space, a question related to the Berge conjecture on lens space surgeries is to determine all knots realizing the minimal rational…
Naturality in sutured monopole and instanton homology
John A. Baldwin, Steven Sivek
Kronheimer and Mrowka defined invariants of balanced sutured manifolds using monopole and instanton Floer homology. Their invariants assign isomorphism classes of modules to balanc…
Sutured Khovanov homology distinguishes braids from other tangles
J. Elisenda Grigsby, Yi Ni
We show that the sutured Khovanov homology of a balanced tangle in the product sutured manifold D x I has rank 1 if and only if the tangle is isotopic to a braid.
Sutured Khovanov homology, Hochschild homology, and the Ozsvath-Szabo spectral sequence
Denis Auroux, J. Elisenda Grigsby, Stephan M. Wehrli
In 2001, Khovanov and Seidel constructed a faithful action of the (m+1)-strand braid group on the derived category of left modules over a quiver algebra, A_m. We interpret the Hoch…