Graph-skein modules of three-manifolds

Research output: Chapter in Book/Report/Conference proceedingChapter


Our main purpose is to introduce the theory of graph-skein modules of three-manifolds. This theory associates to each oriented three-manifold M an algebraic object (a module or an algebra) which is defined by considering the set of all ribbon graphs embedded in M modulo local linear skein relations. This idea is inspired by Przytycki's theory of skein modules which is also known as algebraic topology based on knots. Historically, this theory appeared as a generalization of the quantum invariants of links in the three-sphere to links in an arbitrary three-manifold. In this paper, we review the construction of the Kauffman bracket skein module and investigate its relationship with our graph-skein modules. We compute the graph-skein algebra in few cases. As an application we introduce new criteria for symmetries of spatial graphs which improve some results obtained earlier. The proof of these criteria is based on some easy calculation in the graph-skein module of the solid torus.

Original languageEnglish
Title of host publicationHandbook of Material Science Research
PublisherNova Science Publishers, Inc.
Number of pages17
ISBN (Print)9781607417989
Publication statusPublished - 2010

ASJC Scopus subject areas

  • General Materials Science


Dive into the research topics of 'Graph-skein modules of three-manifolds'. Together they form a unique fingerprint.

Cite this