Universal quadratic forms and Whitney tower intersection invariants

James Conant; Rob Schneiderman; Peter Teichner

doi:10.2140/gtm.2012.18.35

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arXiv · 1207.0109

Universal quadratic forms and Whitney tower intersection invariants

James Conant·Rob Schneiderman·Peter Teichner

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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.

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James Conant, Rob Schneiderman, Peter Teichner. 2012-06-30. Universal quadratic forms and Whitney tower intersection invariants. https://doi.org/10.2140/gtm.2012.18.35

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