Trivalent Graphs, Volume Conjectures and Character Varieties
DSpace at IIT Bombay
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Title |
Trivalent Graphs, Volume Conjectures and Character Varieties
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Creator |
NAWATA, S
PICHAI, R ZODINMAWIA |
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Subject |
quantum invariants of trivalent graphs
generalized volume conjecture AJ conjecture character varieties POLYNOMIALS SYMBOLS KNOTS |
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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.
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Publisher |
SPRINGER
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Date |
2014-12-28T14:33:20Z
2014-12-28T14:33:20Z 2014 |
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Type |
Article
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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 |
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Language |
English
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