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

 

Higher-dimensional linking integrals


Authors: Clayton Shonkwiler and David Shea Vela-Vick
Journal: Proc. Amer. Math. Soc. 139 (2011), 1511-1519
MSC (2010): Primary 57Q45; Secondary 57M25, 53C20
Published electronically: October 1, 2010
MathSciNet review: 2748445
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Abstract: We derive an integral formula for the linking number of two submanifolds of the $ n$-sphere $ S^n$, of the product $ S^n \times \mathbb{R}^m$, and of other manifolds which appear as ``nice'' hypersurfaces in Euclidean space. The formulas are geometrically meaningful in that they are invariant under the action of the special orthogonal group on the ambient space.


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Additional Information

Clayton Shonkwiler
Affiliation: Department of Mathematics, Haverford College, Haverford, Pennsylvania 19041
Email: cshonkwi@haverford.edu

David Shea Vela-Vick
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: shea@math.columbia.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10603-2
PII: S 0002-9939(2010)10603-2
Keywords: Gauss linking integral, linking number
Received by editor(s): September 8, 2009
Received by editor(s) in revised form: April 29, 2010
Published electronically: October 1, 2010
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.