Stably irreducible surfaces in S⁴

Charles Livingston

Vol. 116 (1985), No. 1, 77–84

DOI: 10.2140/pjm.1985.116.77

Abstract

It is shown by example that there are embedded surfaces in S⁴ which cannot be decomposed as the connected sum of a knotted surface of lower genus and an unknotted surface. In addition it is shown that there are distinct embeddings of surfaces into S⁴ such that the complements of the surfaces have the same fundamental groups. The results are generalized to a stable setting. All groups that appear are classical knot groups.

Mathematical Subject Classification 2000

Primary: 57R40

Milestones

Received: 16 May 1983

Revised: 7 July 1983

Published: 1 January 1985