I just found out the very sad news that John Stallings passed away last week after a long illness. Stallings made a number of important contributions to topology, including proving that a 3-manifold is a surface bundle if and only if there is a homomorphism from its fundamental group onto the integers whose kernel is finitely generated. This implies, among other things, that if a 3-manifold has fundamental group isotopic to a surface bundle then it is a surface bundle, which was important in forming the strong analogy that currently exists between 3-manifold topology and group theory.

Stallings also wrote a somewhat infamous (and hard to track down) paper called “How not to prove the Poincare conjecture” which reduces the Poincare conjecture to an algebra-intenive conjecture about Heegaard splittings(!). This is by no means a complete account of Stallings work, but I’m sure many accounts of his life and work will be written in the future.

If anyone wants to send a note of condolence to the family, the Berkeley math department has suggested they be sent to his nephew, Sandy Wilbourn, who had been taking care of him. You can get Sandy’s e-mail from me or probably from Ian Agol (who forwarded me the announcement) or from the Berkeley math department.

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Hi Jesse. Stallings’ paper that you mention is on his webpage. Here’s a link: http://math.berkeley.edu/~stall/notPC.pdf

He was quite a character and will surely be missed by anyone that has ever met him, however incidently.

Comment by chanho — December 1, 2008 @ 4:37 pm |

Very sad indeed. In the long tradition of trying to claim great mathematicians for one’s own field, I often think that Stallings was the first geometric group theorist. And ‘How not to prove the Poincare Conjecture’ is undoubtedly the funniest mathematics paper ever published. The last sentence on page one always makes me laugh out loud.

Comment by Henry Wilton — December 1, 2008 @ 6:37 pm |