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Trivalent Graphs, Volume Conjectures and Character Varieties

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Title Trivalent Graphs, Volume Conjectures and Character Varieties
 
Creator NAWATA, S
PICHAI, R
ZODINMAWIA
 
Subject quantum invariants of trivalent graphs
generalized volume conjecture
AJ conjecture
character varieties
POLYNOMIALS
SYMBOLS
KNOTS
 
Description The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) are extended to colored quantum invariants of the theta and tetrahedron graph. The character variety of the fundamental group of the complement of a trivalent graph with E edges in S (3) is a Lagrangian subvariety of the Hitchin moduli space over the Riemann surface of genus g = E/3 + 1. For the theta and tetrahedron graph, we conjecture that the configuration of the character variety is locally determined by large color asymptotics of the quantum invariants of the trivalent graph in terms of complex Fenchel-Nielsen coordinates. Moreover, the q-holonomic difference equation of the quantum invariants provides the quantization of the character variety.
 
Publisher SPRINGER
 
Date 2014-12-28T14:33:20Z
2014-12-28T14:33:20Z
2014
 
Type Article
 
Identifier LETTERS IN MATHEMATICAL PHYSICS, 104(10)1303-1316
0377-9017
1573-0530
http://dx.doi.org/10.1007/s11005-014-0713-2
http://dspace.library.iitb.ac.in/jspui/handle/100/16763
 
Language English