There is a relation between the generalized Property R Conjecture and the Schoenflies Conjecture that suggests a new line of attack on the latter. The new approach gives a quick proof of the genus 2 Schoenflies Conjecture and suffices to prove the genus 3 case, even in the absence of new progress on the generalized Property R Conjecture.
Cite this article
Martin Scharlemann, Generalized Property R and the Schoenflies Conjecture. Comment. Math. Helv. 83 (2008), no. 2, pp. 421–449DOI 10.4171/CMH/131