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.