Universal quadratic forms and Whitney tower intersection invariants
Abstract
The first part of this paper exposits a simple geometric description of the Kirby-Siebenmann invariant of a 4--manifold in terms of a quadratic refinement of its intersection form. This is the first in a sequence of higher-order intersection invariants of Whitney towers studied by the authors, particularly for the 4--ball. 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. As a corollary we obtain a short exact sequence that has been essential in the understanding of Whitney towers in the 4--ball.
Cite
@article{arxiv.1207.0109,
title = {Universal quadratic forms and Whitney tower intersection invariants},
author = {James Conant and Rob Schneiderman and Peter Teichner},
journal= {arXiv preprint arXiv:1207.0109},
year = {2016}
}
Comments
This paper subsumes the second half (Section 7) of the previously posted paper "Universal Quadratic Forms and Untwisting Whitney Towers" (http://arxiv.org/abs/1101.3480)