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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Splicing and the $ SL_2({\mathbb{C}})$ Casson invariant


Authors: Hans U. Boden and Cynthia L. Curtis
Journal: Proc. Amer. Math. Soc. 136 (2008), 2615-2623
MSC (2000): Primary 57M27; Secondary 57M25, 57M05
Published electronically: March 14, 2008
MathSciNet review: 2390534
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Abstract: We establish a formula for the $ SL_2({\mathbb{C}})$ Casson invariant of spliced sums of homology spheres along knots. Along the way, we show that the $ SL_2({\mathbb{C}})$ Casson invariant vanishes for spliced sums along knots in $ S^3$.


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Additional Information

Hans U. Boden
Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1 Canada
Email: boden@mcmaster.ca

Cynthia L. Curtis
Affiliation: Department of Mathematics and Statistics, The College of New Jersey, Ewing, New Jersey 08628
Email: ccurtis@tcnj.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09233-2
PII: S 0002-9939(08)09233-2
Keywords: Casson invariant, character variety, spliced sum.
Received by editor(s): March 28, 2007
Published electronically: March 14, 2008
Additional Notes: The first named author was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.