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arXiv · 2606.00687

A topological classification of generating functions

Sylvain Courte·Vivek Shende
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Abstract

From a generating function for a Legendrian in a $1$-jet bundle, we may extract the following topological information: (1) a trivialization of the stable Gauss map, (2) the sheaf of sub-level-set stable cohomotopies, and (3) an identification of the microlocalization of the latter with the J-homomorphism image of the former. Here we show that in fact (1), (2), (3) completely classify generating functions up to the classical equivalence relations of stabilization and fiberwise diffeomorphism.

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Sylvain Courte, Vivek Shende. 2026-05-30. A topological classification of generating functions. https://arxiv.org/abs/2606.00687

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