Skip to main content Accessibility help
×
Home

Homology Invariants

  • Richard Hartley (a1) and Kunio Murasugi (a1)

Extract

There have been few published results concerning the relationship between the homology groups of branched and unbranched covering spaces of knots, despite the fact that these invariants are such powerful invariants for distinguishing knot types and have long been recognised as such [8]. It is well known that a simple relationship exists between these homology groups for cyclic covering spaces (see Example 3 in § 3), however for more complicated covering spaces, little has previously been known about the homology group, H1(M) of the branched covering space or about H1(U), U being the corresponding unbranched covering space, or about the relationship between these two groups.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Homology Invariants
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Homology Invariants
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Homology Invariants
      Available formats
      ×

Copyright

References

Hide All
1. Brody, E. J., The topological classification of the lens spaces, Annals of Mathematics 71 (1960), 163184.
2. Burde, G., On branched coverings of S3, Can. J. Math. 23 (1971), 8489.
3. Burnside, W., Theory of groups of finite order (Dover Publications, Inc. Second edition, 1911).
4. Fox, R. H., A quick trip through knot theory, Topology of three manifolds and related topics Prentice Hall, 1962), 120167.
5. Hartley, R. and Murasugi, K., Covering linkage invariants, Can. J. Math. 29 (1977), 13121339.
6. MacLane, S., Categories for the working mathematician (Springer-Verlag, New York, 1971).
7. Perko, K. A., Jr., Octahedral knot covers, Knots, groups and 3-manifolds (Papers dedicated to the memory of Fox, R. H., ed. L. P. Neuwirth), Annals of Math. Studies 84 (1975), 4750.
8. Reidemeister, K., Knoten und Verkettungen, Math. Zeit. 29 (1929), 713729.
9. Riley, R., Homomorphisms of knot groups on finite groups, Mathematics of Computation, 25 (1971), 603619.
10. Riley, R., Hecke invariants of knot groups, Glasgow Math. J. 15 (1974), 1726.
11. Spanier, E. H., Algebraic topology (McGraw-Hill Book Company, New York, 1966).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Homology Invariants

  • Richard Hartley (a1) and Kunio Murasugi (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed