## Bohr Topologies on Abelian Groups |

**Ken Kunen**

March 23, 1997

3:00 pm

Bailey Hall 201

Refreshments in the common room at 2:45

This subject goes back to the work of Harald Bohr in the 1920s and 30s. IfGis any abstract group, the Bohr topology onGis the coarsest topology which makes every group homomorphisms fromGinto any compact topological group continuous. This definition seems simple enough, and is contained in most texts on harmonic analysis, but the topology has remained rather intractable, even for reasonable groups. For example, until recently, it was unknown whether all countably infinite abelian groups had homeomorphic Bohr topologies. I have now shown this to be false, but it is still unknown whether the Bohr topology on the integers is homeomorphic to the Bohr topology on the rationals. My talk will try to give some "picture" of what the Bohr topology "looks" like, both on the integers, and on those few groups where it its structure is well understood.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

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