John R. Stallings

John Robert Stallings Jr. ( born 1935 in Morrilton, Arkansas, † 24 November 2008) was an American mathematician who worked on geometric topology and algebra.

Life

Stallings studied at Princeton University ( one of his fellow students was John Milnor ) and was there in 1959 at Ralph Fox doctorate ( Some Topological proofs and extensions of Grushko 's Theorem ). He was a professor at the University of Berkeley. 1961/62 and 1971 he worked at the Institute for Advanced Study.

In 1960 he proved independently by Stephen Smale the Poincaré conjecture for dimensions greater than 6 His proof was extended in 1962 by Erik Christopher Zeeman on the dimensions 5 and 6. Stallings also formulated purely algebraic ( group-theoretic ) assumptions, the equivalent to the Poincaré conjecture (as he proved with Jaco ).

According to Stallings, the Poincaré conjecture is equivalent to the following theorem ( conjecture of Stallings ):

Be an orientable two-dimensional manifold ( surface ) of the genus, and free groups of rank and a surjective homomorphism of the first fundamental group of on. Then there is a non-trivial element of the core of which is represented by a simple closed curve.

In 1970 he received the Cole prize in algebra with Richard Swan for the proof that finitely generated free groups are characterized in that they have cohomological dimension 1.

In 1970 he was invited speaker at the International Congress of Mathematicians in Nice (Group theory and 3- manifolds ) and 1962 in Stockholm ( Topological unknottedness of Certain spheres ).

Writings

• Stephen M. Gersten: Combinatorial Group Theory and Topology. Princeton University Press, 1987, ISBN 0-691-08409-2.
• Group Theory and Three-dimensional manifolds. Yale University Press 1971, ISBN 0-300-01397-3.
• Topology of finite graphs, Inventiones Mathematicae, Volume 71, 1983, pp. 551-565