Algebraic & Geometric Topology

Hofer–Zehnder capacity and Bruhat graph

Alexander Caviedes Castro

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We find bounds for the Hofer–Zehnder capacity of spherically monotone coadjoint orbits of compact Lie groups with respect to the Kostant–Kirillov–Souriau symplectic form in terms of the combinatorics of their Bruhat graphs. We show that our bounds are sharp for coadjoint orbits of the unitary group and equal in that case to the diameter of a weighted Cayley graph.

Article information

Algebr. Geom. Topol., Volume 20, Number 2 (2020), 565-600.

Received: 2 February 2017
Revised: 4 December 2018
Accepted: 19 April 2019
First available in Project Euclid: 30 April 2020

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35] 57R17: Symplectic and contact topology
Secondary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]

symplectic capacities coadjoint orbits Bruhat graph Hofer–Zehnder capacity


Caviedes Castro, Alexander. Hofer–Zehnder capacity and Bruhat graph. Algebr. Geom. Topol. 20 (2020), no. 2, 565--600. doi:10.2140/agt.2020.20.565.

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