2 7 M ay 2 00 9 Cell Complexes for Arrangements with Group Actions ∗

1 M ay 2 00 8 RANDOM WALKS , ARRANGEMENTS , CELL COMPLEXES , GREEDOIDS , AND SELF - ORGANIZING LIBRARIES

The starting point is the known fact that some much-studied random walks on permutations, such as the Tsetlin library, arise from walks on real hyperplane arrangements. This paper explores similar walks on complex hyperplane arrangements. This is achieved by involving certain cell complexes naturally associated with the arrangement. In a particular case this leads to walks on libraries with sev...

ar X iv : 1 70 5 . 03 17 4 v 1 [ m at h . R T ] 9 M ay 2 01 7 PYRAMIDS AND 2 - REPRESENTATIONS

We describe a diagrammatic procedure which lifts strict monoidal actions from additive categories to categories of complexes avoiding any use of direct sums. As an application, we prove that every simple transitive 2-representation of the 2-category of projective bimodules over a finite dimensional algebra is equivalent to a cell 2-representation.

1 9 M ay 2 00 6 Euler complexes and geometry of modular varieties A . B . Goncharov

2 3 M ay 2 00 7 Braid cobordisms , triangulated categories , and flag varieties Mikhail Khovanov and Richard

We argue that various braid group actions on triangulated categories should be extended to projective actions of the category of braid cobordisms and illustrate how this works in examples. We also construct actions of both the affine braid group and the braid cobordism category on the derived category of coherent sheaves on the cotangent bundle to the full flag variety.

ar X iv : m at h / 05 12 49 7 v 4 [ m at h . A T ] 8 M ay 2 00 7 MOMENT - ANGLE COMPLEXES , MONOMIAL IDEALS , AND MASSEY PRODUCTS

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...