AN SL2(ℂ) ALGEBRO-GEOMETRIC INVARIANT OF KNOTS-Reference-Cited by-同舟云学术

AN SL2(ℂ) ALGEBRO-GEOMETRIC INVARIANT OF KNOTS

Published:2011-09 Issue:09 Volume:22 Page:1209-1230
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

LI WEIPING¹,WANG QINGXUE²

Affiliation:

1. Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, USA

2. School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China

Abstract

In this paper, we define a new algebro-geometric invariant of three-manifolds resulting from Dehn surgery along a hyperbolic knot complement in S3. We establish a Casson-type invariant for these three-manifolds. In the last section, we explicitly calculate the character variety of the figure-eight knot and discuss some applications, as well as the computation of our new invariants for some three-manifolds resulting from Dehn surgery along the figure-eight knot.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X11007240

Reference18 articles.

1. S. Boyer, Handbook of Geometric Topology, eds. R. J. Daverman and R. B. Sher (North-Holland, Amsterdam, 2002) pp. 165–218.

2. On Simple Points Of Character Varieties Of 3-Manifolds

3. A Proof of the Finite Filling Conjecture

4. The classification of exceptional Dehn surgeries on 2-bridge knots

5. Plane curves associated to character varieties of 3-manifolds

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Canonical components of character varieties of arithmetic two-bridge link complements;European Journal of Mathematics;2023-05-22

2. An $$SL_{2}(\mathbb{C})$$ Topological Invariant of Knots;Springer Proceedings in Mathematics & Statistics;2014