By Kuhnel W., Lutz F. H.
A triangulation of a manifold (or pseudomanifold) is termed a good triangulation if any simplexwise linear embedding into any Euclidean area is tight. Tightness of an embedding signifies that the inclusion of any sublevel chosen through a linear practical is injective in homology and, for this reason, topologically crucial. Tightness is a generalization of convexity, and the tightness of a triangulation is a reasonably restrictive estate. We supply a evaluate on all identified examples of tight triangulations and formulate a (computer-aided) enumeration theorem for the case of at so much 15 vertices and the presence of a vertex-transitive automorphism team. Altogether, six new examples of tight triangulations are offered, a vertex-transitive triangulation of the easily attached homogeneous 5-manifold SU(3)/SO(3) with vertex-transitive motion, non-symmetric 12-vertex triangulations of , and non-symmetric triangulations of on thirteen vertices.
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Extra resources for A Census of Tight Triangulations
E A D I P A Start at one of the four corner letters and spiral clockwise round the perimeter, finishing at the centre letter to spell out a nine-letter word. You must provide the missing letters. 38 Ultimate IQ Tests 4 5 6 Which number is the odd one out? 9654 4832 5945 7642 7963 8216 3649 Which two words are closest in meaning? qualified, practicable, puissant, feasible, mundane, fine Identify two words (one from each set of brackets) that have a connection (analogy) with the words in capitals and relate to them in the same way.
Every letter is used once each and all letters are consecutive. 30 ? Draw the missing figure in the above sequence. 31 abashed, derail, little, ? What comes next? mellow, entail, leader, elicit, status 32 Produce an eight-letter word by joining together two of these four-letter sets. 33 cred, agon, lues, once, deva, some, come, pent 20 14 12 24 33 3 10 16 15 18 17 7 4 8 5 1 9 30 36 39 21 13 2 6 11 What number is three places away from itself plus three, two places away from itself multiplied by two, two places away from itself less four and two places away from itself divided by three?
Mellow, entail, leader, elicit, status 32 Produce an eight-letter word by joining together two of these four-letter sets. 33 cred, agon, lues, once, deva, some, come, pent 20 14 12 24 33 3 10 16 15 18 17 7 4 8 5 1 9 30 36 39 21 13 2 6 11 What number is three places away from itself plus three, two places away from itself multiplied by two, two places away from itself less four and two places away from itself divided by three? 43 44 Ultimate IQ Tests 34 ? What comes next? A B C D E 35 What percentage of the figure is shaded?
A Census of Tight Triangulations by Kuhnel W., Lutz F. H.