Second cohomology classes of the group of C 1 -flat diffeomorphisms

Tomohiko Ishida[1]

  • [1] The University of Tokyo Graduate School of Mathematical Sciences Komaba, Meguro-ku ,Tokyo 153-8914 (Japan)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 1, page 77-85
  • ISSN: 0373-0956

Abstract

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We study the cohomology of the group consisting of all C ∞ -diffeomorphisms of the line, which are C 1 -flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.

How to cite

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Ishida, Tomohiko. "Second cohomology classes of the group of $C^1$-flat diffeomorphisms." Annales de l’institut Fourier 62.1 (2012): 77-85. <http://eudml.org/doc/251083>.

@article{Ishida2012,
abstract = {We study the cohomology of the group consisting of all $C^\infty $-diffeomorphisms of the line, which are $C^1$-flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.},
affiliation = {The University of Tokyo Graduate School of Mathematical Sciences Komaba, Meguro-ku ,Tokyo 153-8914 (Japan)},
author = {Ishida, Tomohiko},
journal = {Annales de l’institut Fourier},
keywords = {cohomology of diffeomorphism groups; flat diffeomorphism; Massey product; flat diffeomorphisms; Massey products},
language = {eng},
number = {1},
pages = {77-85},
publisher = {Association des Annales de l’institut Fourier},
title = {Second cohomology classes of the group of $C^1$-flat diffeomorphisms},
url = {http://eudml.org/doc/251083},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Ishida, Tomohiko
TI - Second cohomology classes of the group of $C^1$-flat diffeomorphisms
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 1
SP - 77
EP - 85
AB - We study the cohomology of the group consisting of all $C^\infty $-diffeomorphisms of the line, which are $C^1$-flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.
LA - eng
KW - cohomology of diffeomorphism groups; flat diffeomorphism; Massey product; flat diffeomorphisms; Massey products
UR - http://eudml.org/doc/251083
ER -

References

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  1. Kazuhiko Fukui, Homologies of the group Diff ∞ ( R n , 0 ) and its subgroups, J. Math. Kyoto Univ. 20 (1980), 475-487 Zbl0476.57016MR591806
  2. I. M. Gelʼfand, D. B. Fuks, Cohomologies of the Lie algebra of formal vector fields, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 322-337 Zbl0216.20302MR266195
  3. L. V. Goncharova, The cohomologies of Lie algebras of formal vector fields on the line, Funct. Anal. and Appl. 7 (1973), 91-97, 194–203 Zbl0284.17006
  4. David Kraines, Massey higher products, Trans. Amer. Math. Soc. 124 (1966), 431-449 Zbl0146.19201MR202136
  5. D. Millionschikov, Algebra of formal vector fields on the line and Buchstaber’s conjecture, Funct. Anal. Appl. 43 (2009), 264-278 Zbl1257.17032MR2596653
  6. Floris Takens, Normal forms for certain singularities of vectorfields, Ann. Inst. Fourier (Grenoble) 23 (1973), 163-195 Zbl0266.34046MR365620
  7. F. V. Weinstein, Filtering bases: a tool to compute cohomologies of abstract subalgebras of the Witt algebra, Unconventional Lie algebras 17 (1993), 155-216, Amer. Math. Soc., Providence, RI Zbl0801.17022MR1254731

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