Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
A strong Haken theorem

Martin Scharlemann

Algebraic & Geometric Topology 24 (2024) 717–753
Abstract

Suppose M = A TB is a Heegaard split compact orientable 3–manifold and S M is a reducing sphere for M. Haken (1968) showed that there is then also a reducing sphere S for the Heegaard splitting. Casson and Gordon (1987) extended the result to –reducing disks in M and noted that in both cases S is obtained from S by a sequence of operations called 1–surgeries. Here we show that in fact one may take S = S.

Keywords
Heegaard splitting, compression body, reducing disks and spheres
Mathematical Subject Classification
Primary: 57K35
References
Publication
Received: 8 April 2020
Revised: 1 August 2022
Accepted: 16 August 2022
Published: 12 April 2024
Authors
Martin Scharlemann
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA
United States

Open Access made possible by participating institutions via Subscribe to Open.