Open đ-Spin Theory I: Foundations
- 15 February 2021
- journal article
- research article
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2022 (14), 10458-10532
- https://doi.org/10.1093/imrn/rnaa345
Abstract
We lay the foundation for a version of r-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of r-spin disks, their moduli space, and the Witten bundle; we show that the moduli space is a compact smooth orientable orbifold with corners, and we prove that the Witten bundle is canonically relatively oriented relative to the moduli space. In the sequel to this paper, we use these constructions to define open r-spin intersection theory and relate it to the Gelfand-Dickey hierarchy, thus providing an analog of Witten's r-spin conjecture in the open setting.Keywords
Funding Information
- Ministry of Science and Higher Education (075-2019-1675)
- Division of Mathematical Sciences (1810969)
- Weizmann Institute of Science
- Walter Haefner Stiftung
- Israel Science Foundation (335/19)
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