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Morimichi Kawasaki
기하학 수리물리 연구단
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Bavard's duality theorem on conjugation-invariant norms

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Title
Bavard's duality theorem on conjugation-invariant norms
Author(s)
MORIMICHI KAWASAKI
Publication Date
2017-05
Journal
PACIFIC JOURNAL OF MATHEMATICS, v.288, no.1, pp.157 - 170
Publisher
PACIFIC JOURNAL MATHEMATICS
Abstract
Bavard proved a duality theorem between commutator length and quasimorphisms. Burago, Ivanov and Polterovich introduced the notion of a conjugation-invariant norm which is a generalization of commutator length. Entov and Polterovich proved Oh-Schwarz spectral invariants are subsetcontrolled quasimorphisms, which are generalizations of quasimorphisms. We prove a Bavard-type duality theorem between subset-controlled quasimorphisms on stable groups and conjugation-invariant (pseudo)norms. We also pose a generalization of our main theorem and prove stably nondisplaceable subsets of symplectic manifolds are heavy in a rough sense if that generalization holds. © 2017 Mathematical Sciences Publishers
URI
http://pr.ibs.re.kr/handle/8788114/3580
DOI
10.2140/pjm.2017.288.157
ISSN
0030-8730
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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