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Symmetric Whitney tower cobordism for bordered 3-manifolds and links


Author: Jae Choon Cha
Journal: Trans. Amer. Math. Soc. 366 (2014), 3241-3273
MSC (2010): Primary 57M25, 57M27, 57N70
Published electronically: February 6, 2014
MathSciNet review: 3180746
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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.


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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

DOI: https://doi.org/10.1090/S0002-9947-2014-06025-X
Keywords: Whitney towers, gropes, link concordance, homology cobordism, amenable $L^2$-signatures
Received by editor(s): July 11, 2012
Received by editor(s) in revised form: November 10, 2012
Published electronically: February 6, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.