|
|||||
|
|
|
|
|
|
|
|
|
The
$\mathit{SL}(2,{\mathbb C})$ Casson invariant for Dehn
surgeries on two-bridge knots
Hans U Boden and Cynthia L Curtis |
|
Algebraic & Geometric Topology 12 (2012) 2095–2126
|
Abstract |
|
We investigate the behavior of the Casson invariant for –manifolds obtained by Dehn surgery along two-bridge knots. Using the results of Hatcher and Thurston, and also results of Ohtsuki, we outline how to compute the Culler–Shalen seminorms, and we illustrate this approach by providing explicit computations for double twist knots. We then apply the surgery formula of Curtis [Topology 40 (2001), 773–787] to deduce the Casson invariant for the –manifolds obtained by –Dehn surgery on such knots. These results are applied to prove nontriviality of the Casson invariant for nearly all –manifolds obtained by nontrivial Dehn surgery on a hyperbolic two-bridge knot. We relate the formulas derived to degrees of –polynomials and use this information to identify factors of higher multiplicity in the –polynomial, which is the –polynomial with multiplicities as defined by Boyer–Zhang. |
PDF Access Denied
Warning: We have not been able to recognize your IP address 47.88.87.18 as that of a subscriber to this journal. Online access to the content of recent issues is by subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form.
Or, visit our subscription page for instructions on purchasing a subscription. You may also contact us at contact@msp.org or by using our contact form.
Or, you may purchase this single article for USD 29.95:
Keywords
Casson invariant, character variety, two-bridge knot
|
References |
Publication
Received: 21 May 2012
Revised: 5 July 2012
Accepted: 28 July 2012
Published: 3 December 2012
|
Authors |
| Hans U Boden | |
| Mathematics & Statistics McMaster University 1280 Main St. W. Hamilton, Ontario L8S 4K1 Canada |
|
| http://www.math.mcmaster.ca/~boden/index.html | |
| Cynthia L Curtis | |
| Mathematics & Statistics The College of New Jersey PO Box 7718 Ewing, NJ 08628 USA |
|
|
