Journal of Symplectic Geometry

Volume 19 (2021)

Number 2

Rel–$C^\infty$ structures on Gromov–Witten moduli spaces

Pages: 413 – 473



Mohan Swaminathan (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)


We show that moduli spaces of transversely cut-out (perturbed) pseudo-holomorphic curves in an almost complex manifold carry canonical relative smooth structures (“relative to the moduli space of domain curves”). The main point is that these structures can be characterized by a universal property. The tools required are ordinary gluing analysis combined with some fundamental results from the polyfold theory of Hofer–Wysocki–Zehnder.

Received 22 November 2019

Accepted 30 September 2020

Published 27 May 2021