Symmetric Whitney tower cobordism for bordered 3-manifolds and links
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Abstract:
We introduce the notion of a symmetric Whitney tower cobordism between bordered 3-manifolds, aiming at the study of homology cobordism and link concordance. It is motivated by the symmetric Whitney tower approach to slicing knots and links initiated by T. Cochran, K. Orr, and P. Teichner. We give amenable Cheeger-Gromov $\rho$-invariant obstructions to bordered 3-manifolds being Whitney tower cobordant. Our obstruction is related to and generalizes several prior known results, and also gives new interesting cases. As an application, our method applied to link exteriors reveals new structures on (Whitney tower and grope) concordance between links with nonzero linking number, including the Hopf link.References
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Additional Information
- Jae Choon Cha
- Affiliation: Department of Mathematics, POSTECH, Pohang 790–784, Republic of Korea – and – School of Mathematics, Korea Institute for Advanced Study, Seoul 130–722, Republic of Korea
- Email: jccha@postech.ac.kr
- Received by editor(s): July 11, 2012
- Received by editor(s) in revised form: November 10, 2012
- Published electronically: February 6, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 3241-3273
- MSC (2010): Primary 57M25, 57M27, 57N70
- DOI: https://doi.org/10.1090/S0002-9947-2014-06025-X
- MathSciNet review: 3180746