The rational blowup and torus-surgery conjecture for simply connected smooth 4-manifolds
The rational blowup and torus-surgery conjecture for simply connected smooth 4-manifolds
Let and be homeomorphic simply connected smooth -manifolds. A torus surgery is a surgery on an embedded torus of square , and a rational blowup or rational blowdown is the corresponding rational modification of a smooth -manifold.
Rational blowup and torus-surgery conjecture. and are related via a sequence of surgeries on tori of square , rational blowups, and rational blowdowns.
This is presented as a slight weakening of the preceding torus-surgery conjecture, allowing rational blowups and rational blowdowns as additional operations. The source does not state that it has been resolved, so it remains open.
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Sources & referencesView supporting material
Primary source
Ronald Fintushel and Ronald J. Stern, “Six Lectures on Four 4-Manifolds”, arXiv:math/0610700 (2007).
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