dorsal/arxiv
View SchemaRings of $SL_2({\mathbb C})$-Characters and the Kauffman Bracket Skein Module
| Authors | Doug Bullock |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9604014 |
| URL | https://arxiv.org/abs/q-alg/9604014 |
Abstract
Let $M$ be a compact orientable 3-manifold. The set of characters of $SL_2({\mathbb C})$ representations of the fundamental group of $M$ 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 making the module into 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.
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"abstract": "Let $M$ be a compact orientable 3-manifold. The set of characters of\n$SL_2({\\mathbb C})$ representations of the fundamental group of $M$ forms a\nclosed affine algebraic set. We show that its coordinate ring is isomorphic to\na specialization of the Kauffman bracket skein module modulo its nilradical.\nThis is accomplished by making the module into a combinatorial analog of the\nring, in which tools of skein theory are exploited to illuminate relations\namong characters. We conclude with an application, proving that a small\nmanifold\u0027s specialized module is necessarily finite dimensional.",
"arxiv_id": "q-alg/9604014",
"authors": [
"Doug Bullock"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Rings of $SL_2({\\mathbb C})$-Characters and the Kauffman Bracket Skein Module",
"url": "https://arxiv.org/abs/q-alg/9604014"
},
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