Cohomology equations and commutators of germs of contact diffeomorphisms

Augustin Banyaga; Rafael De La Llave; C. Eugene Wayne

doi:10.1090/S0002-9947-1989-0935530-7

Cohomology equations and commutators of germs of contact diffeomorphisms

Augustin Banyaga
, Rafael De La Llave
, C. Eugene Wayne

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study the group of germs of contact diffeomorphisms at a fixed point. We prove that the abelianization of this group is isomorphic to the multiplicative group of real positive numbers. The principal ingredient in this proof is a version of the Sternberg linearization theorem in which the conjugating diffeomorphism preserves the contact structure.

Original language	English (US)
Pages (from-to)	755-779
Number of pages	25
Journal	Transactions of the American Mathematical Society
Volume	312
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1989-0935530-7
State	Published - Apr 1989

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-1989-0935530-7

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title = "Cohomology equations and commutators of germs of contact diffeomorphisms",

abstract = "We study the group of germs of contact diffeomorphisms at a fixed point. We prove that the abelianization of this group is isomorphic to the multiplicative group of real positive numbers. The principal ingredient in this proof is a version of the Sternberg linearization theorem in which the conjugating diffeomorphism preserves the contact structure.",

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T1 - Cohomology equations and commutators of germs of contact diffeomorphisms

AU - Banyaga, Augustin

AU - De La Llave, Rafael

AU - Eugene Wayne, C.

PY - 1989/4

Y1 - 1989/4

N2 - We study the group of germs of contact diffeomorphisms at a fixed point. We prove that the abelianization of this group is isomorphic to the multiplicative group of real positive numbers. The principal ingredient in this proof is a version of the Sternberg linearization theorem in which the conjugating diffeomorphism preserves the contact structure.

AB - We study the group of germs of contact diffeomorphisms at a fixed point. We prove that the abelianization of this group is isomorphic to the multiplicative group of real positive numbers. The principal ingredient in this proof is a version of the Sternberg linearization theorem in which the conjugating diffeomorphism preserves the contact structure.

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UR - https://www.scopus.com/pages/publications/8744241464#tab=citedBy

U2 - 10.1090/S0002-9947-1989-0935530-7

DO - 10.1090/S0002-9947-1989-0935530-7

M3 - Article

AN - SCOPUS:8744241464

SN - 0002-9947

VL - 312

SP - 755

EP - 779

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

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Cohomology equations and commutators of germs of contact diffeomorphisms

Abstract

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