Kodai Mathematical Journal

New proofs of theorems of Kathryn Mann

Shigenori Matsumoto

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Abstract

We give a shorter proof of the following theorem of Kathryn Mann [M]: the identity component of the group of the compactly supported Cr diffeomorphisms of Rn cannot admit a nontrivial Cp-action on S1, provided n ≥ 2, rn + 1 and p ≥ 2. We also give a new proof of another theorem of Mann [M]: any nontrivial homomorphism from the group of the orientation preserving Cr diffeomorphisms of the circle to the group of Cp diffeomorphisms of the circle is the conjugation of the standard inclusion by a Cp diffeomorphism, if rp, r ≠ 2 and p ≠ 1.

Article information

Source
Kodai Math. J., Volume 37, Number 2 (2014), 427-433.

Dates
First available in Project Euclid: 3 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1404393896

Digital Object Identifier
doi:10.2996/kmj/1404393896

Mathematical Reviews number (MathSciNet)
MR3229085

Zentralblatt MATH identifier
1297.57069

Citation

Matsumoto, Shigenori. New proofs of theorems of Kathryn Mann. Kodai Math. J. 37 (2014), no. 2, 427--433. doi:10.2996/kmj/1404393896. https://projecteuclid.org/euclid.kmj/1404393896


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