On some Graphs Related to Regular, Oriented Triangular Maps

AbstractWe examine the graphψ(G,λ),where the vertices are given by the elements of the conjugacy classλof the finite groupG,and then adjacency (∼) given byv∼u⇔bothuv2andvu2are involutions andu≠v.In particular, under certain conditions on the pair (G, λ)we may derive fromψ(G,λ)a second graphξ(G,λ)which constitutes disjoint copies of underlying graphs of certain regular oriented triangular maps

Matrix factorizations and link homology

For each positive integer n the HOMFLY polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a doubly-graded homology theory of links with this polynomial as the Euler characteristic. The core of our construction utilizes the theory of matrix factorizations, which provide a linear algebra description of maximal Cohen-Macaulay modules on isolated hypersurface singularities.Comment: 108 pages, 61 figures, latex, ep