Symmetric Whitney tower cobordism for bordered 3-manifolds and links

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We introduce a notion of 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 Cochran, Orr, and 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.