Rings of SL2(
$\Bbb{C}$ )-characters and the Kauffman bracket skein module |
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Authors: | D Bullock |
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Institution: | (1) Boise State University, Boise, ID 83725, USA, e-mail: bullock@math.idbsu.edu, US |
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Abstract: | Let M be a compact orientable 3-manifold. The set of characters of SL
2()-representations of forms a closed affine algebraic set. We show that its coordinate ring is isomorphic to a specialization of the Kauffman bracket
skein module, modulo its nilradical. This is accomplished by realizing the module as a combinatorial analog of the ring in
which tools of skein theory are exploited to illuminate relations among characters. We conclude with an application, proving
that a small manifold's specialized module is necessarily finite dimensional.
Received: April 18, 1996 |
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Keywords: | , Knot, link, skein theory, representation theory, 3-manifold, |
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