460 research outputs found
Symmetric groups and checker triangulated surfaces
We consider triangulations of surfaces with edges painted three colors so
that edges of each triangle have different colors. Such structures arise as
Belyi data (or Grothendieck dessins d'enfant), on the other hand they enumerate
pairs of permutations determined up to a common conjugation. The topic of these
notes is links of such combinatorial structures with infinite symmetric groups
and their representations.Comment: 20p., 5 fi
Rigid C^*-tensor categories of bimodules over interpolated free group factors
Given a countably generated rigid C^*-tensor category C, we construct a
planar algebra P whose category of projections Pro is equivalent to C. From P,
we use methods of Guionnet-Jones-Shlyakhtenko-Walker to construct a rigid
C^*-tensor category Bim whose objects are bifinite bimodules over an
interpolated free group factor, and we show Bim is equivalent to Pro. We use
these constructions to show C is equivalent to a category of bifinite bimodules
over L(F_infty).Comment: 50 pages, many figure
Contact handles, duality, and sutured Floer homology
We give an explicit construction of the Honda--Kazez--Mati\'c gluing maps in
terms of contact handles. We use this to prove a duality result for turning a
sutured manifold cobordism around, and to compute the trace in the sutured
Floer TQFT. We also show that the decorated link cobordism maps on the hat
version of link Floer homology defined by the first author via sutured manifold
cobordisms and by the second author via elementary cobordisms agree.Comment: 86 pages, 54 figures, to appear in Geometry and Topolog
- …