Result: Valuations on the character variety: Newton polytopes and residual Poisson bracket
Title:
Valuations on the character variety: Newton polytopes and residual Poisson bracket
Authors:
Contributors:
Simon, Christopher-Lloyd
Source:
Geometry & Topology. 28:593-625
Publication Status:
Preprint
Publisher Information:
Mathematical Sciences Publishers, 2024.
Publication Year:
2024
Subject Terms:
[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA], Goldman Poisson bracket, measured lamination, Geometric Topology (math.GT), 01 natural sciences, Mathematics - Geometric Topology, real tree, symplectic structure, Character variety, skein algebra, FOS: Mathematics, Newton polytope, surface group, [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], 0101 mathematics, valuation, [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], [MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
Document Type:
Academic journal
Article
File Description:
application/pdf
Language:
English
ISSN:
1364-0380
1465-3060
1465-3060
DOI:
10.2140/gt.2024.28.593
DOI:
10.48550/arxiv.2104.04340
Access URL:
Rights:
CC BY
Accession Number:
edsair.doi.dedup.....3c4803c22404663ea960d81b6d91f032
Database:
OpenAIRE
Further Information
We study the space of measured laminations ML on a closed surface from the valuative point of view. We introduce and study a notion of Newton polytope for an algebraic function on the character variety. We prove for instance that trace functions have unit coefficients at the extremal points of their Newton polytope. Then we provide a definition of tangent space at a valuation and show how the Goldman Poisson bracket on the character variety induces a symplectic structure on this valuative model for ML. Finally we identify this symplectic space with previous constructions due to Thurston and Bonahon.
25 pages, 7 figures