the following “influential papers” are listed as relevant for Edward Witten receiving the Fields Medal in 1990.
First of all
Supersymmetry and Morse theory, J. Differential Geom. Volume 17, Number 4 (1982), 661-692. (Euclid)
This discusses deformations of supersymmetric quantum mechanics on a Riemannian manifold and how its supersymmetric ground states are related to the Morse theory of a deformation function. The way this supersymmetric quantum mechanics appears as the point-particle limit of the type II superstring is explained at the end of
Global anomalies in string theory, in W. Bardeen and A. White (eds.) Symposium on Anomalies, Geometry, Topology, pp. 61–99. World Scientific, 1985
Finally Atiyah’s section 2 mentions
Elliptic genera and quantum field theory, Comm. Math. Phys. 109 (1987)
And various articles on the foundations of topological field theory such as
Topological quantum field theory, Comm. Math. Phys. Volume 117, Number 3 (1988), 353-386 (Euclid)
On the structure of the topological phase of two dimensional gravity Nuclear Phys, B 340 (1990) 281 (scans)
Quantum field theory and the Jones polynomial, Comm, Math, Phys, 121 (1989) 351
on the quantization of 3d Chern-Simons theory, its Jones polynomial knot invariant quantum observables and its holographic relation to the quantization of the WZW model (the string propagating on a suitable Lie group manifold).
clearly, this list is supposed to be expanded, eventually…