Advanced Studies in Pure Mathematics

Thurston's h-principle for 2-dimensional foliations of codimension greater than one

Yoshihiko Mitsumatsu and Elmar Vogt

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Abstract

We recreate an unpublished proof of William Thurston from the early 1970's that any smooth 2-plane field on a manifold of dimension at least 4 is homotopic to the tangent plane field of a foliation.

Article information

Source
Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, T. Asuke, S. Matsumoto and Y. Mitsumatsu, eds. (Tokyo: Mathematical Society of Japan, 2017), 181-209

Dates
Received: 26 August 2014
Revised: 13 December 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538671766

Digital Object Identifier
doi:10.2969/aspm/07210181

Mathematical Reviews number (MathSciNet)
MR3726709

Zentralblatt MATH identifier
06843305

Subjects
Primary: 57R30: Foliations; geometric theory 57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]
Secondary: 58D05: Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]

Keywords
2-plane fields integrability of plane fields foliated bundles diffeomorphism groups made discrete

Citation

Mitsumatsu, Yoshihiko; Vogt, Elmar. Thurston's h-principle for 2-dimensional foliations of codimension greater than one. Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, 181--209, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07210181. https://projecteuclid.org/euclid.aspm/1538671766


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