Ronald Alan Fintushel (born 1945) is an American mathematician, specializing in low-dimensional
geometric topology (specifically of 4-
manifolds) and the mathematics of
gauge theory.
His research deals with geometric topology, in particular of 4-manifolds (including the computation of Donaldson and Seiberg-Witten invariants) with links to gauge theory,
knot theory, and
symplectic geometry. He works closely with
Ronald J. Stern.
In 1998 he was an Invited Speaker, with Ronald J. Stern, with talk Construction of smooth 4-manifolds at the
International Congress of Mathematicians in Berlin.[3] In 1997 Fintushel received the Distinguished Faculty Award from Michigan State University. In 2016 a conference was held in his honor at Tulane University.[4]
with Stern: Immersed spheres in 4-manifolds and the immersed Thom conjecture, Turkish Journal of Mathematics, vol. 19, 1995, pp. 145–157
with Stern: Donaldson invariants of 4-manifolds with simple type, J. Diff. Geom., vol. 42, 1995, pp. 577–633
with Stern: The blowup formula for Donaldson invariants, Annals of Mathematics, vol. 143, 1996, pp. 529–546
arXiv
with Stern: Rational blowdowns of smooth 4-manifolds, Journal of Differential Geometry, vol. 46, 1997, pp. 181–235
arXiv
with Stern: Surfaces in 4-manifolds, Math. Res. Letters, vol. 4, 1997, pp. 907–914
arXiv
with Stern: Knots, links, and 4-manifolds, Inventiones mathematicae, vol. 134, 1998, pp. 363–400,
arXiv
with Stern:
Constructions of smooth 4-manifolds. Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 443–452
with Stern: Symplectic surfaces in a fixed homology class, J. Diff. Geom., vol. 52, 2000, pp. 203–222
with Stern: Families of simply connected 4-manifolds with the same Seiberg-Witten invariants, Topology, vol. 43, 2004, pp. 1449–1467
with Stern: Invariants for Lagrangian tori, Geom. Topol., vol. 8, 2004, pp., 947-968
arXiv
with Stern:
Tori in symplectic 4-manifolds, Geometry and Topology Monographs, vol. 7, 2004, Proceedings of the Casson Fest, pp. 311–333
with Stern, B. D. Park: Reverse engineering small 4-manifolds, Algebraic & Geometric Topology, vol. 7, 2007, pp. 2103–2116
arXiv
with Stern: Six Lectures on Four 4-manifolds, Low dimensional topology, IAS/Park City Math. Ser. 15, Amer. Math. Soc., Providence, RI, 2009, pp. 265–315
^Fintushel, Ronald; Stern, Ronald J. (1998).
"Construction of smooth 4-manifolds". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II. pp. 443–452.