From e01fb3d8bbed3a12dcb20637f0a4ab0ec2328f66 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Antonia=20P=C3=A9rez-Cerezo?= Date: Fri, 26 Apr 2024 22:14:51 +0200 Subject: [PATCH] Separate out discrete morse theory --- README.md | 12 ++++++++++++ scripts/README.md | 15 +++++++++++++++ .../20/gALLQQaabcffeeffKacacabazbGbGbMaXbOa.poly | 0 .../20/gALLQQaacddeefffqbvaKb9aCbXaybZaZaoa.poly | 0 .../20/gALLQQaacdefeeffPboajbwaBbkbBava3b2a.poly | 0 .../20/gALLQQaacdfefeff2aKa7a1aHa5aSboaebeb.poly | 0 .../20/gALMMQaacceeffff2aoa7aaaaaEbHaHapbTb.poly | 0 .../20/gAMvQQaabceeffff2aoaqbab1b2a1bjagbxb.poly | 0 .../20/gAvPQQaadefeffef2boaUb2bYb2brarabbba.poly | 0 .../21/gALAQPaacddeeeffyaca0b0bgbKb0biagaba.poly | 0 .../21/gALLQQaabcefefffJafafabaaawb-aQabbQb.poly | 0 .../21/gALLQQaabdeeffffqbgaca1b0baaLanbgbCa.poly | 0 .../21/gALLQQaacddfefffKacajbKaKaKboanbSbnb.poly | 0 .../21/gALLQQaaddefeeffPbganbLbraaaraXaxaqb.poly | 0 .../21/gALLQQaadeffeeffqbgaaaJaEb0aJacaKbSb.poly | 0 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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 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. + + diff --git a/scripts/README.md b/scripts/README.md index c570427..b74625e 100644 --- a/scripts/README.md +++ b/scripts/README.md @@ -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` + + +### 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 +``` diff --git a/triangulations/S^4/20/gALLQQaabcffeeffKacacabazbGbGbMaXbOa.poly b/triangulations/S^4-discretemorse/20/gALLQQaabcffeeffKacacabazbGbGbMaXbOa.poly similarity index 100% rename from triangulations/S^4/20/gALLQQaabcffeeffKacacabazbGbGbMaXbOa.poly rename to triangulations/S^4-discretemorse/20/gALLQQaabcffeeffKacacabazbGbGbMaXbOa.poly diff --git a/triangulations/S^4/20/gALLQQaacddeefffqbvaKb9aCbXaybZaZaoa.poly b/triangulations/S^4-discretemorse/20/gALLQQaacddeefffqbvaKb9aCbXaybZaZaoa.poly similarity index 100% rename from triangulations/S^4/20/gALLQQaacddeefffqbvaKb9aCbXaybZaZaoa.poly rename to 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