Celebratio Mathematica

article M. H. Freedman, V. S. Krushkal, and P. Teichner: “Van Kampen’s embedding obstruction is incomplete for 2-complexes in \( \mathbf{R}^ 4 \),” 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

incollection M. Freedman, R. Hain, and P. Teichner: “Betti number estimates for nilpotent groups,” pp. 413–434 in Fields Medallists’ lectures. Edited by M. Atiyah and D. Iagolnitzer. World Scientific Series in 20th Century Mathematics 5. World Scientific (River Edge, NJ), 1997. MR 1622914

We prove an extension of the following result of Lubotzky and Magid on the rational cohomology of a nilpotent group \( G \): if \( b_1 < \infty \) and \( G\otimes\mathbb{Q} \neq 0 \), \( \mathbb{Q} \), \( \mathbb{Q}^2 \), then \( b_2 > b_1^2/4 \). Here the \( b_i \) are the rational Betti numbers of \( G \) and \( G\otimes\mathbb{Q} \) denotes the Malcev-completion of \( G \). In the extension, the bound is improved when we know that all relations of \( G \) all have at least a certain commutator length. As an application of the refined inequality, we show that each closed oriented 3-manifold falls into exactly one of the following classes: it is a rational homology 3-sphere, or it is a rational homology \( \mathbb{S}^1\times\mathbb{S}^2 \), or it has the rational homology of one of the oriented circle bundles over the torus (which are indexed by an Euler number \( n\in\mathbb{Z} \), e.g. \( n=0 \) corresponds to the 3-torus) or it is of general type by which we meant that the rational lower central series of the fundamental group does not stabilize. In particular, any 3-manifold group which allows a maximal torsion-free nilpotent quotient admits a rational homology isomorphism to a torsion-free nilpotent group.

M. F. Atiyah	Related	Volume
Peter Teichner	Related
Richard M. Hain	Related
Daniel Iagolnitzer	Related

year	title	people

			clear

Michael H. Freedman

Complete Bibliography

Works connected to Peter Teichner

Filter the Bibliography List