A FORMULA FOR THE CASSON INVARIANT BY KAUFFMAN BRACKET SKEIN ALGEBRAS (Topology and Analysis of Discrete Groups and Hyperbolic Spaces)

Abstract

We give a formula for the Casson invariant using $zeta$' : mathcal{I}($Sigma$_{g, 1}) rightarrow (F^{3}S($Sigma$_{g, 1})/F^{5}S($Sigma$_{g, 1}), bch), where (S($Sigma$), {F^{n}S($Sigma$_{g, 1})}_{ngeq 0}) is the filtered Kauffman bracket skein algebra of a surface $Sigma$_{g, 1} of genus g with nonempty connected boundary defined in [2]. Here Let mathcal{I}($Sigma$_{g, 1}) be the Torelli group of $Sigma$_{g_{)}1}.