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math.GT2026
On possible values of the signature of flat unitary bundles over compact surfaces
Inkang Kim, Pierre Pansu, Xueyuan Wan
We determine all possible signatures of flat Hermitian bundles over compact, connected, oriented surfaces of positive genus with nonempty boundary. If has genus …
math.GT2022★ 1 cited
Signature for flat unitary bundles over surfaces with boundary
Inkang Kim, Pierre Pansu, Xueyuan Wan
This paper deals with the representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the sign…
math.GT2021★ 1 cited
Signature, Toledo invariant and surface group representations in the real symplectic group
Inkang Kim, Pierre Pansu, Xueyuan Wan
In this paper, by using Atiyah-Patodi-Singer index theorem, we obtain a formula for the signature of a flat symplectic vector bundle over a surface with boundary, which is related…