TY - JOUR
T1 - The group of strong symplectic homeomorphisms in the L∞-metric
AU - Banyaga, Augustin
AU - Tchuiaga, Stéphane
N1 - Funding Information:
Acknowledgments. We would like to thank Peter Spaeth and Stefan Müller for helpful hints, advice, and improvements of the preliminary drafts of this paper. The second author thanks the Germany Office of University Exchanges (DAAD) and the International Centre of Theoretical Physics (ICTP) for financial support of his research at the Institute of Mathematics and Physical Sciences (IMSP).
Publisher Copyright:
© de Gruyter 2014.
PY - 2014/7/1
Y1 - 2014/7/1
N2 - The group SSympeo(M, ω) of strong symplectic homeomorphisms or group of ssympeomorphisms of a closed connected symplectic manifold (M, ω) was defined and studied in [2], [3]. In these papers the author uses the L(1,∞)-metric on the group Iso(M, ω) of all symplectic isotopies. In this paper we study the set SSympeo(M, ω)∞ of ssympeomorphisms in the L∞-metric. We prove the equality between SSympeo(M, ω) and SSympeo(M, ω)∞. This generalizes Müller's result [6] asserting that Hameo(M, ω) = Hameo(M, ω)∞.
AB - The group SSympeo(M, ω) of strong symplectic homeomorphisms or group of ssympeomorphisms of a closed connected symplectic manifold (M, ω) was defined and studied in [2], [3]. In these papers the author uses the L(1,∞)-metric on the group Iso(M, ω) of all symplectic isotopies. In this paper we study the set SSympeo(M, ω)∞ of ssympeomorphisms in the L∞-metric. We prove the equality between SSympeo(M, ω) and SSympeo(M, ω)∞. This generalizes Müller's result [6] asserting that Hameo(M, ω) = Hameo(M, ω)∞.
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U2 - 10.1515/advgeom-2013-0041
DO - 10.1515/advgeom-2013-0041
M3 - Article
AN - SCOPUS:84925344899
VL - 14
SP - 523
EP - 539
JO - Advances in Geometry
JF - Advances in Geometry
SN - 1615-715X
IS - 3
ER -