Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Tuesday, December 7, 2004 - 07:00
Location: 
Kidd 350 (<b>NOTE: Unusual location</b>)

Speaker Info

Institution: 
University of Ljubljana
Abstract: 

There has been a long history of construction of wild (nonstandard) Cantor sets in R^n with certain additional properties. It is possible to construct examples that have simply connected complement, and it is possible to construct other examples that are rigidly embedded. (This means that any homeomorphism of R^n to itself that takes the Cantor set to itself, is in fact the identity on the Cantor Set.) Recently, Garity, Repovs and Zeljko were able to construct examples in R^3 that are both rigid and have simply connected complement. I will briefly discuss the history of such examples, and will provide more details on the new construction. The proofs for rigidity for previous examples rely heavily on linking arguments and cannot be used in construction of Cantor sets with simply connected complement. A notion of a local genus introduced by M. Zeljko is used to overcome this difficulty.