Commentarii Mathematici Helvetici


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Volume 83, Issue 2, 2008, pp. 421–449
DOI: 10.4171/CMH/131

Generalized Property R and the Schoenflies Conjecture

Martin Scharlemann[1]

(1) Department of Mathematics, University of California, CA 93106, SANTA BARBARA, UNITED STATES

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.

Keywords: Schoenflies Conjecture, Heegaard splitting, framed surgery, critical level embedding, Property R

Scharlemann Martin: Generalized Property R and the Schoenflies Conjecture. Comment. Math. Helv. 83 (2008), 421-449. doi: 10.4171/CMH/131