Representations of the Kauffman bracket skein algebra I: invariants and miraculous cancellations

• 成果类型: Article
• 署名作者: Bonahon, Francis; Wong, Helen
• 署名单位: University of Southern California; Carleton College
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0611-y
• 发表日期: 2016
• 页码: 195-243
• 关键词: quantization; SPACES; MODULES

摘要

We study finite-dimensional representations of the Kauffman bracket skein algebra of a surface S. In particular, we construct invariants of such irreducible representations when the underlying parameter is a root of unity. The main one of these invariants is a point in the character variety consisting of group homomorphisms from the fundamental group to , or in a twisted version of this character variety. The proof relies on certain miraculous cancellations that occur for the quantum trace homomorphism constructed by the authors. These miraculous cancellations also play a fundamental role in subsequent work of the authors, where novel examples of representations of the skein algebra are constructed.