Robert Bieri

Robert Bieri (born January 31, 1945 in Zurich ) is a Swiss mathematician and professor emeritus at the Goethe University in Frankfurt am Main .

Bieri received his doctorate in 1972 under Beno Eckmann at the ETH Zurich ("Groups with Poincaré duality"). He deals with geometric, topological and homological methods in group theory .

Working together with Eckmann, he introduced the concept of Poincaré duality for groups and classified resolvable groups with Poincaré duality. With Eckmann he introduced a generalization (groups with homological duality). With John RJ Groves he also introduced concepts of tropical geometry to group theory at an early stage ( George Bergman is considered to be the pioneer of tropical geometry with a paper from 1971). In 1980, together with Ralph Strebel, he introduced the geometric invariant for metabelian groups G, which he generalized to a further class of groups in 1987 with Walter David Neumann and Raph Strebel ( Bieri-Neumann-Strebel invariant ). ${\displaystyle \Sigma (G)}$

Fonts (selection)

Unless mentioned in the individual evidence.

• Normal subgroups in duality groups and in groups of cohomological dimension 2. In: Journal of Pure and Applied Algebra. Volume 7, 1976, pp. 35-51.
• A connection between the integral homology and the center of a rational linear group. In: Mathematical Journal . Volume 170, 1980, pp. 263-266.
• with John RJ Groves : Metabelian groups of type FPm are virtually of type FP. In: Proceedings of the London Mathematical Society . Volume 45, 1982, pp. 365-384.
• mit Burkhardt Renz: Valuations on free resolutions and higher geometric invariants of groups. In: Commentarii Mathematici Helvetici . Volume 63, 1988, pp. 464-497.
• with Ross Geoghegan: Connectivity properties of group actions on non-positively curved spaces. In: Memoirs of the AMS. 765, 2003.
• with Ross Geoghegan: Limit sets for modules over groups on CAT (0) spaces - from the Euclidean to the hyperbolic. In: Proceedings of the London Mathematical Society. Volume 112, 2016, pp. 1059-1102.

Web links

• Robert Bieri on the website of the University of Frankfurt with comments on selected works

Individual evidence

1. ↑ Date of birth according to Kürschner's Scholarly Calendar 2009.
2. ^ Robert Bieri in the Mathematics Genealogy Project (English) .
3. ^ Robert Bieri: Groups with Poincaré duality. In: Commentarii Mathematici Helvetici . Volume 47, 1974, pp. 373-396. Corresponds to the dissertation from 1972. Francis EA Johnson and Charles TC Wall introduced the concept independently and with a different definition : Francis EA Johnson, Charles TC Wall : On groups satisfying Poincaré Duality. In: Annals of Mathematics . Volume 69, 1972, pp. 592-598.
4. ^ Robert Bieri, Beno Eckmann : Groups with homological duality generalizing Poincaré duality. In: Inventiones Mathematicae . Volume 20, 1973, pp. 103-124.
5. ^ Robert Bieri, John RJ Groves : The geometry of the set of characters induced by valuations. In: Journal for pure and applied mathematics . Volume 347, 1984, pp. 168-195.
6. ^ Robert Bieri, Ralph Strebel : Valuations and finitely presented metabelian groups. In: Proceedings of the London Mathematical Society . Volume 41, 1980, pp. 439-464.
7. ^ Robert Bieri, Walter David Neumann, Ralph Strebel: A geometric invariant of discrete groups. In: Inventiones Mathematicae. Volume 90, 1987, pp. 451-477.