Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×

Online ordering will be unavailable from 17:00 GMT on Friday, April 25 until 17:00 GMT on Sunday, April 27 due to maintenance. We apologise for the inconvenience.

  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • On the Asphericity of Knot Complements

  • Vo Thanh Liem, Gerard A. Venema
  • Journal:
    Canadian Journal of Mathematics / Volume 45 / Issue 2 / 01 April 1993
    Published online by Cambridge University Press:
    20 November 2018, pp. 340-356
    Print publication:
    01 April 1993
    • Article
      • You have access
    • PDF
    • Export citation

  • Two examples of topological embeddings of S2 in S4 are constructed. The first has the unusual property that the fundamental group of the complement is isomorphic to the integers while the second homotopy group of the complement is nontrivial. The second example is a non-locally flat embedding whose complement exhibits this property locally.

    Two theorems are proved. The first answers the question of just when good π1 implies the vanishing of the higher homotopy groups for knot complements in S4. The second theorem characterizes local flatness for 2-spheres in S4 in terms of a local π1 condition.