An integer valued SU(3) Casson invariant

Abstract

We define an integer valued invariant of homology spheres using the methods of SU (3) gauge theory and study its behavior under orientation reversal and connected sum.

Splitting the spectral flow and the SU(3) Casson invariant for spliced sums

“…Remark As noted above, this result also computes the integer-valued SU.3/ Casson invariant SU.3/ .M / of [3]. While the results of [4; 5] show that neither the SU.3/ Casson invariant has finite-type, the above theorem shows that the behavior of SU.3/ and SU.3/ under splicing is very similar to that of the finite-type invariant of degree three.…”

“…While the integer-valued SU.3/ Casson invariant SU.3/ of Boden, Herald and Kirk [3] is not additive under connected sum, by [3,Theorem 4], the difference SU.3/ 2 2 SU.2/ is, and a natural question to ask is whether it is also additive under spliced sum. In general, the answer is no and we briefly explain why not.…”

The Calderón projector for the odd signature operator and spectral flow calculations in 3-dimensional topology

“…This complicates the construction of a well defined invariant. At this time there are three competing versions of the SU (3) Casson invariant [5,6,13], each one different from the others but all defined using the same basic approach, which we now explain.…”

“…Another construction for a correction term was presented in [6], yielding an integer valued invariant with many nice properties. One sets…”

“…Taubes' article has had a lasting impact on the study of analysis on 3-manifolds and forms the blueprint on which many constructions of topological invariants of 3-manifolds are based. This includes the work of the authors on SU (3) generalizations of Casson's SU (2) invariant, reported on in the articles [5,6,7,8].…”