Kauffman bracket skein module of the connected sum of two projective spaces

2010/08/05 by Maciej Mroczkowski, Mroczkowski, Maciej · 3 citations
Mathematics · Medicine · #57M27 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M27

paper · pdf · doi:10.48550/arxiv.1008.1007

22 pages, 21 figures

arxiv created 2010/08/05 · openalex publication_date 2010/08/05 · arxiv updated 2010/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Diagrams and Reidemeister moves for links in a twisted S¹-bundle over an unorientable surface are introduced. Using these diagrams, we compute the Kauffman Bracket Skein Module (KBSM) of the connected sum of two projective spaces. In particular, we show that it has torsion. We also present a new computation of the KBSM of S¹ x S² and the lens spaces L(p,1).

Cited by

• Dimension of the skein module of a Dehn filling
• An effective proof of finiteness for Kauffman bracket skein modules
• KBSM of lens spaces L(p,2) and L(4k,2k+1)

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