1996/04/20 by Doug Bullock, Bullock, Doug
Mathematics · #57M99 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #msc:57M99 #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9604014
LaTeX2e v1.2, document class amsart.cls with package epsfig, 18 pages, 9 figures
arxiv created 1996/04/20 · openalex publication_date 1996/04/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a compact orientable 3-manifold. The set of characters of SL2(\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.