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Abstract
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Let
be a
symplectic rational surface. We study the space of tamed almost complex structures
using
a fine decomposition via smooth rational curves and a relative version of the infinite
dimensional Alexander–Pontrjagin duality. This decomposition provides new
understandings of both the variation and the stability of the symplectomorphism group
when deforming
. In particular, we
compute the rank of
with
in terms
of the number
of
-symplectic
sphere classes.
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Keywords
symplectomorphism group, almost complex structure, rational
symplectic manifold, Lagrangian root system
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Mathematical Subject Classification 2010
Primary: 32Q65, 53C15, 53D35, 57R17
Secondary: 53D05, 57S05
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Milestones
Received: 22 March 2019
Revised: 3 July 2019
Accepted: 31 August 2019
Published: 12 February 2020
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