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Categorification of the virtual braid groups

Anne-Laure Thiel (2011)

Annales mathématiques Blaise Pascal

We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.

Cell-like resolutions of polyhedra by special ones

Dušan Repovš, Arkady Skopenkov (2000)

Colloquium Mathematicae

Suppose that P is a finite 2-polyhedron. We prove that there exists a PL surjective map f:Q → P from a fake surface Q with preimages of f either points or arcs or 2-disks. This yields a reduction of the Whitehead asphericity conjecture (which asserts that every subpolyhedron of an aspherical 2-polyhedron is also aspherical) to the case of fake surfaces. Moreover, if the set of points of P having a neighbourhood homeomorphic to the 2-disk is a disjoint union of open 2-disks, and every point of P...

Chewing the Khovanov homology of tangles

Magnus Jacobsson (2004)

Fundamenta Mathematicae

We present an elementary description of Khovanov's homology of tangles [K2], in the spirit of Viro's paper [V]. The formulation here is over the polynomial ring ℤ[c], unlike [K2] where the theory was presented over the integers only.

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