TY - JOUR

T1 - Open r-Spin Theory I: Foundations

AU - Buryak, Alexandr

AU - Clader, Emily

AU - Tessler, Ran J.

N1 - Funding Information: The work was supported by the Mathematical Center in Akademgorodok under agreement No. 075-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation (to A.B.); the National Science Foundational Division of Mathematical Sciences, (1810969 to E.C.); the Center for New Scientists of Weizmann Institute (to R.T.); Dr Max Rossler (to R.T.); the Walter Haefner Foundation (to R.T.); the Eidgenossische Technische Hochschule Zurich Foundation (to R.T.); and the Israel Science Foundation (grant 335/19 to R.T.). © 2021 The Author(s). Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

PY - 2022/7/1

Y1 - 2022/7/1

N2 - 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.

AB - 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.

KW - MODULI

KW - CURVES

UR - http://www.scopus.com/inward/record.url?scp=85135697958&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnaa345

DO - 10.1093/imrn/rnaa345

M3 - Article

VL - 2022

SP - 10458

EP - 10532

JO - International mathematics research notices

JF - International mathematics research notices

SN - 1073-7928

IS - 14

M1 - 345

ER -