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An Elliptic Path Fibration and Holomorphic Morita Equivalence
Abstract
We construct an elliptic analogue of the Alekseev-Meinrenken path fibration \cite{alekseev2009atiyah} for a simply connected complex Lie group with a nondegenerate invariant symmetric bilinear form. A natural $2$-form on the correspondence space induces a holomorphic symplectic groupoid over the space of (0,1)-connections and a holomorphic quasi-symplectic groupoid over the holomorphic loop group. The correspondence space defines a principal holomorphic Morita bibundle with compatible differential forms.
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BibTeX
@misc{khazaeipoul2026elliptic,
title = {{An Elliptic Path Fibration and Holomorphic Morita Equivalence}},
author = {Ahmmadreza Khazaeipoul},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33793},
eprint = {2610.33793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33793},
}
RIS
TY - UNPB
TI - An Elliptic Path Fibration and Holomorphic Morita Equivalence
AU - Ahmmadreza Khazaeipoul
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33793
UR - https://arxiv.org/abs/2610.33793
AB - We construct an elliptic analogue of the Alekseev-Meinrenken path fibration \cite{alekseev2009atiyah} for a simply connected complex Lie group with a nondegenerate invariant symmetric bilinear form. A natural $2$-form on the correspondence space induces a holomorphic symplectic groupoid over the space of (0,1)-connections and a holomorphic quasi-symplectic groupoid over the holomorphic loop group. The correspondence space defines a principal holomorphic Morita bibundle with compatible differential forms.
ER -