Separate out discrete morse theory

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Antonia 2024-04-26 22:14:51 +02:00
parent b12461371e
commit e01fb3d8bb
50 changed files with 27 additions and 0 deletions

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@ -38,6 +38,18 @@ These 1464 triangulations have all been shown to be PL-Homeomorphic to
each other using retriangulate, however, polymake has big difficulties each other using retriangulate, however, polymake has big difficulties
in finding the PL-homeomorphisms between them. in finding the PL-homeomorphisms between them.
### S⁴
These 1016 triangulations are triangulations of S⁴ shown to be
PL-homeomorphic to S⁴ using the retriangulate tool, for which no other
methods (bistellar simplification, discrete morse theory) worked.
### S⁴-discretemorse
These 48 triangulations have been shown to be PL-homeomorphic to S⁴ by
finding a spherical discrete morse vector.

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@ -33,3 +33,18 @@ INSERT INTO minimal_triangulations SELECT DISTINCT ON (signature) * FROM triangu
``` ```
Remove combinatorially isomorphic triangulations by running `triangulation_bookkeeping_minimal.pl`, and output sorted by type using `triangulation_bookkeeping_output.pl` Remove combinatorially isomorphic triangulations by running `triangulation_bookkeeping_minimal.pl`, and output sorted by type using `triangulation_bookkeeping_output.pl`
### Spheres
Additionally, sort spheres for which a spherical discrete morse vector was found with
```
for k in $(psql -d researchdata_test -c "SELECT signature FROM complexes WHERE remark = 'discrete_morse';" | grep '^ g' | sed 's/ //g' ) ;
do
p=$(find . -name *$k*);
npt=../S^4-discretemorse/$p;
mkdir -p $(dirname $npt);
mv $p $npt;
done
```