Celebratio Mathematica — Freedman

Topology in dImension 4

Works connected to Peter Teichner

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article M. H. Freedman, V. S. Krushkal, and P. Teichner: “Van Kampen’s embedding obstruction is incomplete for 2-complexes in $R^{4}$ ,” Math. Res. Lett. 1 : 2 (March 1994), pp. 167–176. MR 1266755 Zbl 0847.57005

V. Slava Krushkal	Related
Peter Teichner	Related

article M. H. Freedman and P. Teichner: “4-manifold topology I: Subexponential groups,” Invent. Math. 122 : 3 (1995), pp. 509–529. MR 1359602 Zbl 0857.57017

The technical lemma underlying the 5-dimensional topological $ s $-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating $ \pi_1 $-null immersions of disks. These conjectures are theorems precisely for those fundamental groups (“good groups”) where the $ \pi_1 $-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations: (1) extension and (2) direct limit. The finitely generated groups in thisclass are amenable and no amenable group is known to lie outside this class.

article M. H. Freedman and P. Teichner: “4-Manifold topology II: Dwyer’s filtration and surgery kernels,” Invent. Math. 122 : 1 (1995), pp. 531–557. MR 1359603 Zbl 0857.57018