Generalized Property R and the Schoenflies Conjecture

Scharlemann, Martin

doi:10.4171/CMH/131

Commentarii Mathematici Helvetici

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Volume 83, Issue 2, 2008, pp. 421–449

DOI: 10.4171/CMH/131

Published online: 2008-06-30

Generalized Property R and the Schoenflies Conjecture

Martin Scharlemann^[1]

(1) University of California, 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