Opened 8 years ago
Closed 8 years ago
#13725 closed enhancement (fixed)
sum complexes: another example of simplicial complexes
Reported by: | jhpalmieri | Owned by: | jhpalmieri |
---|---|---|---|
Priority: | minor | Milestone: | sage-5.6 |
Component: | algebraic topology | Keywords: | |
Cc: | tscrim, stumpc5 | Merged in: | sage-5.6.beta2 |
Authors: | John Palmieri | Reviewers: | Travis Scrimshaw |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | #12587 | Stopgaps: |
Description
The attached patch adds a new collection of examples of simplicial complexes called "sum complexes". I'm interested in them because their homology can have large torsion groups relative to the number of vertices. For example:
sage: simplicial_complexes.SumComplex(13, [0,1,2,3,5]).homology(3) C3 x C237 x C706565607945
That's a very large torsion group for a complex with only 13 vertices!
Attachments (2)
Change History (7)
comment:1 Changed 8 years ago by
- Status changed from new to needs_review
comment:2 Changed 8 years ago by
- Cc tscrim stumpc5 added
Changed 8 years ago by
comment:3 Changed 8 years ago by
- Dependencies set to #12587
- Reviewers set to Travis Scrimshaw
Changed 8 years ago by
comment:4 Changed 8 years ago by
- Status changed from needs_review to positive_review
Your patch looks good to me. By the way, since writing my patch, I found an example, simplicial_complexes.SumComplex(13, [0,1,2,3,4,7])
, whose fourth homology group is
C3 x C3 x C37209 x C14755222692546209667
It takes Sage several minutes to calculate this, so we shouldn't add it to the examples, but it's interesting to see how large the torsion can be for a complex with 13 vertices.
comment:5 Changed 8 years ago by
- Merged in set to sage-5.6.beta2
- Resolution set to fixed
- Status changed from positive_review to closed
Hey John,
I'm uploaded a small review patch which tweaks the generation code (basically I removed the temp variable
k
sincelen()
is called only once for the for loop and made the output immutable from #12587), and separates out the doctests into generating the simplicial complex and the homology calculations. If you agree with the changes, feel free to set this to positive review.Best,
Travis
PS - This applied cleanly for me over #12587, and I love the somewhat pathological examples that these simplicial complexes are.