229 citations · 827 across the 21 of their papers we have counts for
7 papers · 1 filter
Invariants of surfaces in smooth 4-manifolds from link homology
Kim Morrison, Kevin Walker, Paul Wedrich
We construct analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of any smooth oriented 4-manifold. The main tools are skein lasagna modules…
Skein lasagna modules and handle decompositions
Ciprian Manolescu, Kevin Walker, Paul Wedrich
The skein lasagna module is an extension of Khovanov-Rozansky homology to the setting of a four-manifold and a link in its boundary. This invariant plays the role of the Hilbert sp…
Man and machine thinking about the smooth 4-dimensional Poincaré conjecture
Michael Freedman, Robert Gompf, Scott Morrison +1
While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincaré conjecture (SPC4) for over 30 years, until recently no invariant has existed…
Positivity of the universal pairing in 3 dimensions
Danny Calegari, Michael Freedman, Kevin Walker
Associated to a closed, oriented surface S is the complex vector space with basis the set of all compact, oriented 3-manifolds which it bounds. Gluing along S defines a Hermitian p…
Fixing the functoriality of Khovanov homology
David Clark, Scott Morrison, Kevin Walker
We describe a modification of Khovanov homology (math.QA/9908171), in the spirit of Bar-Natan (math.GT/0410495), which makes the theory properly functorial with respect to link cob…
Universal manifold pairings and positivity
Michael H Freedman, Alexei Kitaev, Chetan Nayak +3
Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p=<,> w…