55 research outputs found
Categorification of the colored -invariant
We give explicit resolutions of all finite dimensional, simple
-modules. We use these resolutions to categorify the
colored -invariant of framed links via a complex of complexes
of graded -modules.Comment: 39 pages, many figures. Comments welcome
A new way to evaluate MOY graphs
We define a new way to evaluate MOY graphs. We prove that this new evaluation
coincides with the classical evaluation by checking some skein relations. As a
consequence, we prove a formula which relates the and
-evaluations of MOY graphs.Comment: Introduction rewritte
A signature invariant for knotted Klein graphs
We define some signature invariants for a class of knotted trivalent graphs
using branched covers. We relate them to classical signatures of knots and
links. Finally, we explain how to compute these invariants through the example
of Kinoshita's knotted theta graph.Comment: 23 pages, many figures. Comments welcome ! Historical inaccuracy
fixe
A large family of indecomposable projective modules for the Khovanov-Kuperberg algebra of -webs
We recall a construction of Mackaay, Pan and Tubbenhauer of the algebras
which allow to understand the homology for links in a
local way (i.e. for tangles). Then, by studying the combinatorics of the
Kuperberg bracket, we give a large family of non-elliptic webs whose associated
projective -modules are indecomposable.Comment: Minor changes, 21 pages, 24 figure
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