An application of the h-principle to manifold calculus

Apurva Nakade*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 Emb Lag(- , N) is the totally real embeddings functor Emb TR(- , N). More generally, for subsets A of the m-plane Grassmannian bundle Gr(m,TN) for which the h-principle holds for A-directed embeddings, we prove the analyticity of the A-directed embeddings functor EmbA(-,N).

Original languageEnglish (US)
Pages (from-to)309-322
Number of pages14
JournalJournal of Homotopy and Related Structures
Volume15
Issue number2
DOIs
StatePublished - Jun 1 2020
Externally publishedYes

Keywords

  • h-Principle
  • Lagrangian embeddings
  • Manifold calculus
  • Totally real embeddings

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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