1,085 research outputs found
Sl(N) link homology using foams and the Kapustin-Li formula
We use foams to give a topological construction of a rational link homology
categorifying the slN link invariant, for N>3. To evaluate closed foams we use
the Kapustin-Li formula adapted to foams by Khovanov and Rozansky. We show that
for any link our homology is isomorphic to Khovanov and Rozansky's.Comment: The Kapustin-Li formula has been corrected for facets with non-zero
genus and its normalization and some signs have been changed accordingly. 43
pages, lots of figure
Transitive factorizations of permutations and geometry
We give an account of our work on transitive factorizations of permutations.
The work has had impact upon other areas of mathematics such as the enumeration
of graph embeddings, random matrices, branched covers, and the moduli spaces of
curves. Aspects of these seemingly unrelated areas are seen to be related in a
unifying view from the perspective of algebraic combinatorics. At several
points this work has intertwined with Richard Stanley's in significant ways.Comment: 12 pages, dedicated to Richard Stanley on the occasion of his 70th
birthda
Triangulated surfaces in triangulated categories
For a triangulated category A with a 2-periodic dg-enhancement and a
triangulated oriented marked surface S we introduce a dg-category F(S,A)
parametrizing systems of exact triangles in A labelled by triangles of S. Our
main result is that F(S,A) is independent on the choice of a triangulation of S
up to essentially unique Morita equivalence. In particular, it admits a
canonical action of the mapping class group. The proof is based on general
properties of cyclic 2-Segal spaces.
In the simplest case, where A is the category of 2-periodic complexes of
vector spaces, F(S,A) turns out to be a purely topological model for the Fukaya
category of the surface S. Therefore, our construction can be seen as
implementing a 2-dimensional instance of Kontsevich's program on localizing the
Fukaya category along a singular Lagrangian spine.Comment: 55 pages, v2: references added and typos corrected, v3: expanded
version, comments welcom
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