#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### LIBRARY OF TRIANGULATIONS ### ### by Bruno Benedetti and Frank H. Lutz ### ### http://page.math.tu-berlin.de/~lutz/stellar/library_of_triangulations.html ### ### ### ### ### ### name of example: ### ### ### ### knot ### ### ### ### ### ### description: ### ### ### ### simplicial subdivision of Furch's non-constructible knotted hole ball; ### ### the example nc_sphere is derived from the example knot ### ### by adding the cone over its boundary with respect to the vertex 381 ### ### ### ### ### ### properties: ### ### ### ### f=(380,1929,2722,1172), ### ### H_*=(Z,0,0,0), ### ### non-constructible, non-shellable, ### ### admits discrete Morse vector: (1,1,1,0), ### ### claim by Lewiner: (1,0,0,0), ### ### best known lower bound: (1,0,0,0) ### ### ### ### ### ### references: ### ### ### ### M. Hachimori. ### ### Furch's knotted hole ball. ### ### http://infoshako.sk.tsukuba.ac.jp/~hachi/math/library/knot_eng.html ### ### ### ### M. Hachimori. ### ### Simplicial complex library. ### ### http://infoshako.sk.tsukuba.ac.jp/~hachi/math/library/index_eng.html ### ### ### ### M. Hachimori. ### ### Nonconstructible simplicial balls and a way ### ### of testing constructibility. ### ### Discrete Comput. Geom. 22, 223-230 (1999). ### ### ### ### T. Lewiner. ### ### Geometric Discrete Morse Complexes. Dissertation. ### ### Pontifícia Universidade Católica do Rio de Janeiro, 2005, 131 pages. ### ### http://zeus.mat.puc-rio.br/tomlew/pdfs/tomlew_phd_puc.pdf. ### ### ### ### B. Benedetti and F. H. Lutz. ### ### Random discrete Morse theory and a new library of triangulations. ### ### Exp. 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