Stability conditions and the braid group

Stability conditions and the braid group

We find stability conditions ([D2], [Br]) on some derived categories of differential graded modules over a graded algebra studied in [RZ], [KS]. This category arises in both derived Fukaya categories and derived categories of coherent sheaves. This gives the first examples of stability conditions on the A-model side of mirror symmetry, where the triangulated category is not naturally the derive...

The Braid Group of Z

We define quasi-Garside groups and prove a theorem about them parallel to Garside’s result on the word problem for the usual braid groups. We introduce a group which we call the braid group B of Zn, and which bears some resemblance to mapping class groups. We prove that B is a quasi-Garside group. We give a ‘small presentation’ for B.

Filling factors and Braid group

We extract the Braid group structure of a recently derived hierarchy scheme for the filling factors proposed by us which related the Hausdorff dimension, h, to the statistics, ν, of the collective excitations in the context of the Fractional Quantum Hall Effect (FQHE).

Derivative Varieties and the Pure Braid Group

The Hurwitz Action and Braid Group Orderings

In connection with the so-called Hurwitz action of homeomorphisms in ramified covers we define a groupoid, which we call a ramification groupoid of the 2sphere, constructed as a certain path groupoid of the universal ramified cover of the 2-sphere with finitely many marked-points. Our approach to ramified covers is based on cosheaf spaces, which are closely related to Fox’s complete spreads. A ...