Representing elements of π1M3 by fibred knots
Published
Journal Article
Every smooth, closed, orientable manifold of dimension 3 contains a fibred knot, i.e. an imbedded circle K such that M – K is the total space of a fibre bundle over S1 whose fibre F is standard near K. This means the boundary of the closure of F is K so that K is null-homologous in M. A natural problem suggested by Rolfsen (see (2), problem 3·13) is to determine which elements of π1M3 may be represented by fibred knots. We deal with this by proving theTheorem. The collection of all elements of π1 M3 which can be represented by fibred knots is exactly the commutator subgroup [π1 M3, π1 M3].
Full Text
Duke Authors
Cited Authors
- Harer, J
Published Date
- July 1982
Published In
Volume / Issue
- 92 / 1
Start / End Page
- 133 - 138
Published By
Electronic International Standard Serial Number (EISSN)
- 1469-8064
International Standard Serial Number (ISSN)
- 0305-0041
Digital Object Identifier (DOI)
- 10.1017/s030500410005979x
Language
- en