Invariants of homology 3-spheres

Xiao-Song Lin
Department of Mathematics, University of California, Riverside

ABSTRACT


The Casson invariant of homology 3-spheres is known to be the first order perturbative SU(2) quantum invariant. Higher order perturbative invariants are generalizations of the Casson invariants. We will provide an overview of Ohtsuki's proof of the existence of higher order perturbative invariants. Our computation will lead to a congruence relation between the Casson invariant and Ohtsuki's second order invariant. The later thus gives rise to another integer lifting of the Rohklin invariant.