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A unified quantum SO(3) invariant for rational homology 3-spheres


Beliakova, A; Bühler, I; Le, T (2011). A unified quantum SO(3) invariant for rational homology 3-spheres. Inventiones Mathematicae, 185(1):121-174.

Abstract

Given a rational homology 3-sphere M with |H 1 (M,ℤ)|=b and a link L inside M, colored by odd numbers, we construct a unified invariant I M,L belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten-Reshetikhin-Turaev invariants of the pair (M,L). If b=1 and L=∅,I M coincides with Habiro's invariant of integral homology 3-spheres. For b>1, the unified invariant defined by the third author is determined by I M . Important applications are the new Ohtsuki series (perturbative expansions of I M ) dominating quantum SO(3) invariants at roots of unity whose order is not a power of a prime. These series are not known to be determined by the LMO invariant.

Abstract

Given a rational homology 3-sphere M with |H 1 (M,ℤ)|=b and a link L inside M, colored by odd numbers, we construct a unified invariant I M,L belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten-Reshetikhin-Turaev invariants of the pair (M,L). If b=1 and L=∅,I M coincides with Habiro's invariant of integral homology 3-spheres. For b>1, the unified invariant defined by the third author is determined by I M . Important applications are the new Ohtsuki series (perturbative expansions of I M ) dominating quantum SO(3) invariants at roots of unity whose order is not a power of a prime. These series are not known to be determined by the LMO invariant.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > General Mathematics
Language:English
Date:2011
Deposited On:16 Nov 2011 15:45
Last Modified:17 Apr 2024 03:33
Publisher:Springer
ISSN:0020-9910
Additional Information:The original publication is available at www.springerlink.com
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00222-010-0304-5
Related URLs:http://arxiv.org/abs/0801.3893
  • Content: Accepted Version
  • Description: Author manuscript
  • Content: Accepted Version
  • Description: Version 1
  • Content: Accepted Version
  • Description: Version 2
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  • Description: Version 3
  • Content: Published Version
  • Language: English
  • Description: Nationallizenz 142-005