The Gromov width of generalized Bott manifolds

TL;DR

This paper computes the Gromov width of generalized Bott manifolds by analyzing their moment map images, which are polytopes combinatorially equivalent to products of simplices, providing explicit symplectic capacity measurements.

Contribution

It provides a formula for the Gromov width of generalized Bott manifolds based on their defining inequalities, extending symplectic capacity calculations to this class.

Findings

Gromov width expressed in terms of polytope inequalities

Explicit computation for generalized Bott manifolds

Connection between moment map images and symplectic capacities

Abstract

By Delzant's theorem, closed symplectic toric manifolds are classified by the images of moment maps. In the case of a generalized Bott manifold, this image is a polytope $P$ combinatorially equivalent to the product of simplices. We compute the Gromov width of generalized Bott manifolds in terms of the defining inequalities of $P$.