Advanced Studies in Pure Mathematics

A few open problems on characteristic classes of foliations

Shigeyuki Morita

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Abstract

In this paper, we consider a few major open problems in the theory of characteristic classes of foliations. After recalling some history and background of each of these problems, we propose possible approaches to challenge them and present several “sub-problems”.

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), 221-237

Dates
Received: 1 June 2014
Revised: 10 November 2014
First available in Project Euclid: 4 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1538671768

Digital Object Identifier
doi:10.2969/aspm/07210221

Mathematical Reviews number (MathSciNet)
MR3726711

Zentralblatt MATH identifier
1391.58007

Subjects
Primary: 58H10: Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]
Secondary: 57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]

Keywords
foliation Godbillon–Vey class characteristic class $\Gamma$-structure classifying space

Citation

Morita, Shigeyuki. A few open problems on characteristic classes of foliations. Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, 221--237, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07210221. https://projecteuclid.org/euclid.aspm/1538671768


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