Record Details
Simply connected open 3-manifolds with rigid genus one ends
ScholarsArchive at Oregon State University
| Field | Value |
|---|---|
| Title | Simply connected open 3-manifolds with rigid genus one ends |
| Names |
Garity, Dennis
(creator) Repovš, Dušan (creator) Wright, David (creator) |
| Date Issued | 2014-01 (iso8601) |
| Note | This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/journal/13163. |
| Abstract | We construct uncountably many simply connected open 3-manifolds with genus one ends homeomorphic to the Cantor set. Each constructed manifold has the property that any self homeomorphism of the manifold (which necessarily extends to a homeomorphism of the ends) fixes the ends pointwise. These manifolds are complements of rigid generalized Bing-Whitehead (BW) Cantor sets. Previous examples of rigid Cantor sets with simply connected complement in R³ had infinite genus and it was an open question as to whether finite genus examples existed. The examples here exhibit the minimum possible genus, genus one. These rigid generalized BW Cantor sets are constructed using variable numbers of Bing and Whitehead links. Our previous result with Željko determining when BW Cantor sets are equivalently embedded in R³ extends to the generalized construction. This characterization is used to prove rigidity and to distinguish the uncountably many examples. |
| Genre | Article |
| Topic | Open 3-manifold |
| Identifier | Garity, D., Repovš, D., & Wright, D. (2014). Simply connected open 3-manifolds with rigid genus one ends. Revista Matemática Complutense, 27(1), 291-304. doi:10.1007/s13163-013-0117-3 |
