7,381 research outputs found
The complex of pant decompositions of a surface
We exhibit a set of edges (moves) and 2-cells (relations) making the complex
of pant decompositions on a surface a simply connected complex. Our
construction, unlike the previous ones, keeps the arguments concerning the
structural transformations independent from those deriving from the action of
the mapping class group. The moves and the relations turn out to be supported
in subsurfaces with 3g-3+n=1,2 (where g is the genus and n is the number of
boundary components), illustrating in this way the so called Grothendieck
principle.Comment: Minor changes in the introductio
From Operator Algebras to Superconformal Field Theory
We make a review on the recent progress in the operator algebraic approach to
(super)conformal field theory. We discuss representation theory, classification
results, full and boundary conformal field theories, relations to supervertex
operator algebras and Moonshine, connections to subfactor theory and
noncommutative geometry
Endotrivial modules for the sporadic simple groups and their covers
In a step towards the classification of endotrivial modules for quasi-simple
groups, we investigate endotrivial modules for the sporadic simple groups and
their covers. A main outcome of our study is the existence of torsion
endotrivial modules with dimension greater than one for several sporadic groups
with -rank greater than one.Comment: in Journal of Pure and Applied Algebra, published online 19th
February 201
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