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\ ̄t6-Free maps satisfy the homotopy principle

Authors
Journal
Indagationes Mathematicae
0019-3577
Publisher
Elsevier
Publication Date
Volume
9
Issue
1
Identifiers
DOI: 10.1016/s0019-3577(97)87569-6
Disciplines
  • Mathematics

Abstract

Abstract In this short note we show that the space of all \ ̄ t6-free maps of any complex manifold V c into C n is always homotopically equivalent to the space of all sections of the corresponding bundle in the space of jets of smooth maps V c → C n . In particular, the space of all linear ordinary differential equations with complex-valued coefficients on an elliptic curve with the identical monodromy (defined as the conjugacy class in the corresponding loop group) is weakly homotopically equivalent to the space of all based maps of the curve in GL n ( C). The proof is based on Gromov's theory of convex integration, see e.g. [Gr,McD].

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