Erratum : a presentation for Hilden's subgroup of the Braid group
Tawn, Stephen. (2011) Erratum : a presentation for Hilden's subgroup of the Braid group. Mathematical Research Letters, Vol.18 (No.1). pp. 175-180. ISSN 1073-2780Full text not available from this repository.
Official URL: http://www.mathjournals.org/mrl/2011-018-001/2011-...
After publication of  Allen Hatcher found a gap in the proof that the complex Xn is simply connected. This complex is defined in terms of isotopy classes of discs, but the argument uses representatives of the isotopy classes. There was an implicit assumption that for an edge path in the complex there exists sufficiently nice representatives of each isotopy class. In definition 2 of this paper the properties of these representatives will be made explicit. It is clear that such representatives exist for a path, the problem is that for a loop it is not obvious that the representative at the beginning and end can be chosen to coincide. This problem is addressed in Lemma 3. Section 2 of this paper contains the complete proof that Xn is simply connected, incorporating all of the necessary changes.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Library of Congress Subject Headings (LCSH):||Group theory, Braid theory|
|Journal or Publication Title:||Mathematical Research Letters|
|Page Range:||pp. 175-180|
|Version or Related Resource:||Erratum to: Tawn, S. (2008). A presentation for Hilden's subgroup of the braid group. Mathematical Research Letters, 15(5-6), pp. 1277-1293. http://wrap.warwick.ac.uk/id/eprint/28704|
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