Notes for BBS/Polyak-100706-103132.jpg

Abstract: We will discuss a simple combinatorial construction of link and 3-manifold invariants which involves counting trivalent graphs. This construction may be interpreted in terms of counting surfaces of a certain genus and number of boundary components in a Gauss diagram. For 3-manifolds, counting graphs of genus zero and one give the homology and the Casson-Walker invariant respectively.