Dubrovnik VI – Geometric Topology September 30 – October 7, 2007
	ABSTRACTS	pdf-version of this abstract

Dennis Garity^*
Oregon State University, Corvallis, OR, USA

Techniques for determining rigidity of embeddings of Cantor sets

We discuss the techniques used in our proof that there exist rigid wild Cantor sets in R³ with simply connected complement. Previous constructions of rigid Cantor sets using variations on the Antoine construction in R³ had non simply connected complement. The simply connected examples in are constructed using a generalization of a construction of Skora together with a careful analysis of the local genus of points in the Cantor sets.

REFERENCES

R. Skora. Cantor sets in $S^3$ with simply connected complements, Topol. Appl. 24 (1986), 181–188.
M. Željko. Genus of a Cantor Set, Rocky Mountain J. Math., vol. 35, no. 1, 2005.

* This is a joint work with Dušan Repovš and Matjaž Željko.