Journal of Symplectic Geometry

Volume 17 (2019)

Number 3

Thin compactifications and relative fundamental classes

Pages: 703 – 752

DOI: https://dx.doi.org/10.4310/JSG.2019.v17.n3.a4

Authors

Eleny-Nicoleta Ionel (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Thomas H. Parker (Department of Mathematics, Michigan State University, East Lansing, Mich., U.S.A.)

Abstract

We define a notion of relative fundamental class that applies to moduli spaces in gauge theory and in symplectic Gromov–Witten theory. For universal moduli spaces over a parameter space, the relative fundamental class specifies an element of the Čech homology of the compactification of each fiber; it is defined if the compactification is “thin” in the sense that the boundary of the generic fiber has homological codimension at least two.

Received 1 November 2017

Accepted 25 July 2018

Published 9 September 2019