An Application of the $h$-principle to Manifold Calculus

Abstract

Manifold calculus is a form of functor calculus that analyzes contravariant functors from some categories of manifolds to topological spaces by providing analytic approximations to them. In this paper, using the technique of the $h$-principle, we show that for a symplectic manifold $N$, the analytic approximation to the Lagrangian embeddings functor ${\mathrm{Emb}}_{\mathrm{Lag}}(-,N)$ is the totally real embeddings functor ${\mathrm{Emb}}_{\mathrm{TR}}(-,N)$. More generally, for subsets $\mathcal{A}$ of the $m$-plane Grassmannian bundle $\mathrm{Gr}(m,TN)$ for which the $h$-principle holds for $\mathcal{A}$-directed embeddings, we prove the analyticity of the $\mathcal{A}$-directed embeddings functor ${\mathrm{Emb}}_{\mathcal{A}}(-,N)$.

This revised version contains only the main results. Several minor errors have been fixed and the notation is simplified. 12 pages. Journal of Homotopy and Related Structures, 2020

References in corpus (3)

• Spaces of smooth embeddings and configuration categories
• Some finiteness results for groups of automorphisms of manifolds
• An Application of the $h$-principle to Manifold Calculus

Cited by in corpus (1)

• An Application of the $h$-principle to Manifold Calculus