A combinatorial construction of symplectic expansions
Yusuke Kuno
TL;DR
This paper presents a new combinatorial method for constructing symplectic expansions, linking surface topology with formal symplectic geometry through a recurrence formula involving the Baker-Campbell-Hausdorff series.
Contribution
It introduces a novel combinatorial approach to construct symplectic expansions using a recurrence relation, advancing the understanding of surface topology and symplectic geometry.
Findings
Provides a recurrence formula for symplectic expansion construction
Connects surface topology with formal symplectic geometry
Offers a systematic method for symplectic expansion construction
Abstract
The notion of a symplectic expansion directly relates the topology of a surface to formal symplectic geometry. We give a method to construct a symplectic expansion by solving a recurrence formula given in terms of the Baker-Campbell-Hausdorff series.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Algebraic structures and combinatorial models