The rational blowup and torus-surgery conjecture for simply connected smooth 4-manifolds

From papers

Let XX and YY be homeomorphic simply connected smooth 44-manifolds. A torus surgery is a surgery on an embedded torus of square 00, and a rational blowup or rational blowdown is the corresponding rational modification of a smooth 44-manifold.

Rational blowup and torus-surgery conjecture. XX and YY are related via a sequence of surgeries on tori of square 00, 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.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

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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