An \(SL_{2}(\mathbb{C})\) Topological Invariant of Knots

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)


In this note, we show that the \(SL_{2}(\mathbb{C})\) algebro-geometric invariant defined in Li and Wang (Int. J. Math. 22(9):1209–1230, 2011) for knots is indeed an \(SL_{2}(\mathbb{C})\) topological invariant. The main ingredient is our short geometric proof of the coincidence of the algebro-geometric multiplicity and topological multiplicity of the intersection of curves on a smooth surface.


Irreducible Component Topological Invariant Zariski Closure Hyperbolic Structure Intersection Multiplicity 
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The author would like to thank Qingxue Wang and Baosen Wu for many helpful discussions related to this work, and also grateful to Baosen Wu for the proof of Theorem 1.


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© Springer Japan 2014

Authors and Affiliations

  1. 1.Southwest Jiaotong UniversityCollege of MathematicsSichuanPeople’s Republic of China
  2. 2.Department of MathematicsOklahoma State UniversityStillwaterUSA

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