JournalscmhVol. 72 , No. 4DOI 10.1007/s000140050032

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

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.