Not signed in (Sign In)

# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Sign in using OpenID

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 22nd 2020

Page created, but author did not leave any comments.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJul 22nd 2020

needed to record a reference. Now somebody needs to put some content into this entry… :-)

• CommentRowNumber3.
• CommentAuthorDmitri Pavlov
• CommentTimeJul 22nd 2020

Link to Manifold Atlas.

1. Added some content to the idea section.

• CommentRowNumber5.
• CommentAuthorRichard Williamson
• CommentTimeJul 22nd 2020
• (edited Jul 22nd 2020)

In particular, added a construction (with picture in tikz, for my sins!) of lens spaces via integral surgery, which, though completely standard, is not that easy to find in the literature if one does not know where to look.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeNov 18th 2020

added this pointer:

• Michel Boileau, Steven Boyer, Radu Cebanu, Genevieve S. Walsh, Section 3 of: Knot commensurability and the Berge conjecture, Geom. Topol. 16 (2012) 625-664 (arXiv:1008.1034)
• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeNov 18th 2020
• (edited Nov 18th 2020)

added pointer on 3d-3d correspondence for lens spaces:

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeNov 18th 2020

I have added the actual definition to the entry and have organized the previous material into subsections of a “Properties” section.

The paragraph on Dehn surgery seemed to have been lacking the qualifier “coprime”, so I added it.

• CommentRowNumber9.
• CommentAuthorRichard Williamson
• CommentTimeNov 18th 2020
• (edited Nov 18th 2020)

Thanks for the correction! Regarding

are in some sense the simplest

there is at least one precise sense in which this is true, namely Lens spaces are the only 3-manifolds one can obtain by integral Dehn surgery on the unknot except for $S^{3}$ and  $S^{2} \times S^{1}$. In a hurry now, so no time to find a reference, but it might be nice to add this to the entry; it should be in any textbook on geometric topology.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeNov 18th 2020

Okay. I have added the “in some sense” only to make clear that at this point it’s an informal statement. But if it can be made precise further down in the entry, all the better.

Add your comments
• Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
• To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

• (Help)