Symmetric Whitney tower cobordism for bordered 3-manifolds and links

Cha, Jae Choon

doi:10.1090/S0002-9947-2014-06025-X

Symmetric Whitney tower cobordism for bordered 3-manifolds and links
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Trans. Amer. Math. Soc. 366 (2014), 3241-3273 Request permission

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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