Abstract
Let be a connected and locally 1–connected space, and let . A decorated –local system is an –local system on , together with a chosen element of the stalk at each component of .
We study the decorated –character algebra of : the algebra of polynomial invariants of decorated –local systems on . The character algebra is presented explicitly. The character algebra is shown to correspond to the –algebra spanned by collections of oriented curves in modulo local topological rules.
As an intermediate step, we obtain an invariant-theory result of independent interest: a presentation of the algebra of –invariant functions on , where is the tautological representation of .
Citation
Greg Muller. Peter Samuelson. "Character algebras of decorated $\operatorname{SL}_2(C)$–local systems." Algebr. Geom. Topol. 13 (4) 2429 - 2469, 2013. https://doi.org/10.2140/agt.2013.13.2429
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