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arXiv · 2407.10515

On possible values of the signature of flat symplectic bundles over surfaces with boundary

Inkang Kim·Pierre Pansu·Xueyuan Wan
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Abstract

We show that every integer in the interval $[2p\chi(\Sigma), -2p\chi(\Sigma)]$ is achieved by the signature of a rank $2p$ flat symplectic bundle over a surface with boundary $\Sigma$. When $p=1$, one can prescribe the type (elliptic, parabolic, hyperbolic) of the holonomy along the boundary.

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Inkang Kim, Pierre Pansu, Xueyuan Wan. 2024-07-15. On possible values of the signature of flat symplectic bundles over surfaces with boundary. https://arxiv.org/abs/2407.10515

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