Finite slope cyclic surgeries along toroidal Brunnian links and generalized Properties P and R

2015/04/06 by Teruhisa Kadokami, Kadokami, Teruhisa
Mathematics · #57M25 #57M27 #57Q10 #57R65 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1504.01321

openalex publication_date 2015/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let M_λ be the λ-component Milnor link. For λ≥ 3, we determine completely when a finite slope surgery along M_λ yields a lens space including S³ and S¹× S², where \it finite slope surgery implies that a surgery coefficient of every component is not ∞. For λ=3 (i.e. the Borromean rings), there are three infinite sequences of finite slope surgeries yielding lens spaces. For λ≥ 4, any finite slope surgery does not yield a lens space. As a corollary, M_λ for λ≥ 3 does not yield both S³ and S¹× S² by any finite slope surgery. We generalize the results for the cases of \it Brunnian type links and toroidal Brunnian type links (i.e. Brunnian type links including essential tori in the link complement). Our main tools are Alexander polynomials and Reidemeister torsions. Moreover we characterized toroidal Brunnian links and toroidal Brunnian type links in some senses.

Citations

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Dehn Surgery on Knots

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