Topological quantum field theory and hyperkähler geometry
Abstract
Rozansky and Witten proposed a 3dimensional sigmamodel whose target space is a hyperkähler manifold. They conjectured that this theory has an associated TQFT, with Hilbert spaces given by certain cohomology groups of the hyperkähler manifold. On the other hand, there is a certain modified TQFT constructed by Murakami and Ohtsuki using the universal quantum invariant. We explain how the RozanskyWitten TQFT can be obtained from the latter by applying a `hyperkähler weight system'.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2000
 arXiv:
 arXiv:math/0009222
 Bibcode:
 2000math......9222S
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Differential Geometry;
 53C26;
 57R56;
 57M27
 EPrint:
 LaTeX, 26 pages, 13 figures