Orbifold Mapping Spaces via Bibundles
Abstract
The existence of orbifold structures on mapping spaces between orbifolds was established in previous work, notably by W. Chen and B. Chen-Du-Liao. In this paper, we construct an infinite-dimensional orbifold structure on the mapping space in a more geometric way, using bibundles (or Hilsum-Skandalis morphisms), based on Lerman's description of orbifold morphisms. We construct a proper étale (or Fréchet) Lie groupoid representing the mapping space in the Ck, C∞, and Wk,p settings, and show that its Morita equivalence class is independent of the choices of groupoid presentations. Locally, the mapping groupoid is isomorphic to the action groupoid of a finite group, where the finite group is identified with the automorphism group of the corresponding bibundle. This provides a concrete geometric framework for further studies of mapping spaces and moduli spaces on orbifolds, with applications to Floer theory on symplectic orbifolds.
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BibTeX
@misc{sugimoto2026orbifold,
title = {{Orbifold Mapping Spaces via Bibundles}},
author = {Yoshihiro Sugimoto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35435},
eprint = {2609.35435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35435},
}
RIS
TY - UNPB
TI - Orbifold Mapping Spaces via Bibundles
AU - Yoshihiro Sugimoto
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35435
UR - https://arxiv.org/abs/2609.35435
AB - The existence of orbifold structures on mapping spaces between orbifolds was established in previous work, notably by W. Chen and B. Chen-Du-Liao. In this paper, we construct an infinite-dimensional orbifold structure on the mapping space in a more geometric way, using bibundles (or Hilsum-Skandalis morphisms), based on Lerman's description of orbifold morphisms. We construct a proper étale (or Fréchet) Lie groupoid representing the mapping space in the C^k, C^∞, and W^k,p settings, and show that its Morita equivalence class is independent of the choices of groupoid presentations. Locally, the mapping groupoid is isomorphic to the action groupoid of a finite group, where the finite group is identified with the automorphism group of the corresponding bibundle. This provides a concrete geometric framework for further studies of mapping spaces and moduli spaces on orbifolds, with applications to Floer theory on symplectic orbifolds.
ER -