Universal Quadratic Forms and Untwisting Whitney Towers
Abstract
The first part of this paper completes the classification of Whitney towers in the 4-ball that was started in three related papers. We provide an algebraic framework allowing the computations of the graded groups associated to geometric filtrations of classical link concordance by order n (twisted) Whitney towers in the 4-ball. Higher-order Sato-Levine invariants and higher-order Arf invariants are defined and shown to be the obstructions to framing a twisted Whitney tower. In the second part of this paper, a general theory of quadratic forms is developed and then specialized from the non-commutative to the commutative to finally, the symmetric settings. The intersection invariant for twisted Whitney towers is shown to be the universal symmetric refinement of the framed intersection invariant. UPDATE: The results of the first six sections of this paper have been subsumed into the paper "Whitney tower concordance of classical links."
Cite
@article{arxiv.1101.3480,
title = {Universal Quadratic Forms and Untwisting Whitney Towers},
author = {James Conant and Rob Schneiderman and Peter Teichner},
journal= {arXiv preprint arXiv:1101.3480},
year = {2015}
}
Comments
The results of the first six sections of this paper have been subsumed into the paper arXiv:1207.0109 "Whitney tower concordance of classical links." References have been updated