JournalscmhVol. 72, No. 4pp. 521–542

Rings of SL2( C\Bbb{C} )-characters and the Kauffman bracket skein module

  • D. Bullock

    Boise State University, USA
Rings of SL2( $\Bbb{C}$ )-characters and the Kauffman bracket skein module cover
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Abstract

Let M be a compact orientable 3-manifold. The set of characters of SL2(C\Bbb {C})-representations of π1(M)\pi_1(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 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.

Cite this article

D. Bullock, Rings of SL2( C\Bbb{C} )-characters and the Kauffman bracket skein module. Comment. Math. Helv. 72 (1997), no. 4, pp. 521–542

DOI 10.1007/S000140050032