The Universal Perturbative Quantum 3manifold Invariant, RozanskyWitten Invariants, and the Generalized Casson Invariant
Abstract
Let Z^{LMO} be the 3manifold invariant of [LMO]. It is shown that Z^{LMO}(M)=1, if the first Betti number of M, b_{1}(M), is greater than 3. If b_{1}(M)=3, then Z^{LMO}(M) is completely determined by the cohomology ring of M. A relation of Z^{LMO} with the RozanskyWitten invariants Z_{X}^{RW}[M] is established at a physical level of rigour. We show that Z_{X}^{RW}[M] satisfies appropriate connected sum properties suggesting that the generalized Casson invariant ought to be computable from the LMO invariant.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1999
 arXiv:
 arXiv:math/9911049
 Bibcode:
 1999math.....11049H
 Keywords:

 Mathematics  Geometric Topology;
 High Energy Physics  Theory
 EPrint:
 LaTex 62 pages with 4 figures