Bohr Topologies on Abelian Groups
March 23, 1997
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. If G is any abstract group, the Bohr topology on G is the coarsest topology which makes every group homomorphisms from G into 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.
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