Beno Eckmann Quotes

Swiss mathematician (1917–2008)

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Beno Eckmann (31 March 1917 – 25 November 2008) was a Swiss mathematician, known for his research in algebraic topology, homological algebra, group theory, and differential geometry. At the International Congress of Mathematicians he was an invited speaker in 1954 in Amsterdam and a plenary speaker in 1962 in Stockholm. He won the 2008 Albert Einstein Medal.

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Together with many other people and after a long development I could prove that a Poincaré duality group of cohomological dimension 2 is the group of a Riemann surface. That was actually a conjecture of Jean-Pierre Serre. "You have to prove it!" he had always insisted.

Still another important area is Poincaré duality for groups, invented by Robert Bieri and myself. They behave like manifolds: homology, cohomology, you see, in complementary dimensions, but with another dualizing module. Many groups that are interesting in algebraic geometry, group theory or other areas are such duality groups.

We probably all agree that eventually reducing a difficult problem to a "nice" situation is at the heart of mathematics.