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Generating Functions in \\(R^2n\\) and the Hatcher-Waldhausen map
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Paper
Generating Functions in \\(R^2n\\) and the Hatcher-Waldhausen map
2026
Overview
In this paper, we construct a generating function quadratic at infinity for any exact Lagrangian in \\( R^2n\\) that equals \\( R^n\\) outside a compact set. Such a Lagrangian may be viewed as a Lagrangian filling of the standard Legendrian unknot \\(S^n-1\\) in \\(D^2n\\). Generating functions of the type we construct are related to the space \\( M_ınfty\\) considered by Eliashberg and Gromov. We also show that \\( M_ınfty\\) is the homotopy fiber of the so-called Hatcher--Waldhausen map. This further relates the study of exact Lagrangians (and Legendrians) to algebraic K-theory of spaces. Using this and Bökstedt's result that the Hatcher--Waldhausen map is a rational homotopy equivalence, we prove that the stable Lagrangian Gauss map (relative to the boundary) of the Lagrangian is null-homotopic.
Publisher
Cornell University Library, arXiv.org
Subject
