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Knots in Washington XXV dedicated to Herbert Seifert on his 100 birthday. Conference on Knot Theory and its Ramifications
December 7-9, 2007
George Washington University
Washington, DC, USA

Organizers
Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Dan Silver (U. South Al.), Hao Wu (GWU)

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Unified SO(3)-quantum invariants for rational homology 3-spheres.
by
Buehler Irmgard
Winterthurerstrasse 190, 8057 Zuerich, Switzerland
Coauthors: A. Beliakova, T. Le

In 2001, K. Habiro constructed for an integer homology 3-sphere M a unified invariant I_M(q) which, if evaluated at any root of unity, gives the SU(2) Witten-Reshetikhin-Turaev invariant of M at that root. In this talk we extend Habiro's construction to rational homology 3-spheres. More precisely, given a rational homology 3-sphere M with |H_1(M;Z)|=b and an odd divisor c of b, we construct a unified invariant I_{M,c}(q), which dominates the SO(3) WRT invariants of M at all roots of unity whose order r has (r,b)=c.

Date received: November 7, 2007

Copyright © 2007 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cavo-06.