Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
k-Normal surfaces. / Fominykh, Evgeny; Martelli, Bruno.
в: Journal of Differential Geometry, Том 82, № 1, 01.01.2009, стр. 101-114.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - k-Normal surfaces
AU - Fominykh, Evgeny
AU - Martelli, Bruno
PY - 2009/1/1
Y1 - 2009/1/1
N2 - Following Matveev, a k-normal surface in a triangulated 3- manifold is a generalization of both normal and (octagonal) al- most normal surfaces. Using spines, complexity, and Turaev-Viro invariants of 3-manifolds, we prove the following results: • a minimal triangulation of a closed irreducible or a bounded hyperbolic 3-manifold contains no non-trivial k-normal sphere; • every triangulation of a closed manifold with at least 2 tetra- hedra contains some non-trivial normal surface; • every manifold with boundary has only finitely many triangu- lations without non-trivial normal surfaces. Here, triangulations of bounded manifolds are actually ideal tri-angulations. We also calculate the number of normal surfaces of nonnegative Euler characteristics which are contained in the conjecturally minimal triangulations of all lens spaces L p, q .
AB - Following Matveev, a k-normal surface in a triangulated 3- manifold is a generalization of both normal and (octagonal) al- most normal surfaces. Using spines, complexity, and Turaev-Viro invariants of 3-manifolds, we prove the following results: • a minimal triangulation of a closed irreducible or a bounded hyperbolic 3-manifold contains no non-trivial k-normal sphere; • every triangulation of a closed manifold with at least 2 tetra- hedra contains some non-trivial normal surface; • every manifold with boundary has only finitely many triangu- lations without non-trivial normal surfaces. Here, triangulations of bounded manifolds are actually ideal tri-angulations. We also calculate the number of normal surfaces of nonnegative Euler characteristics which are contained in the conjecturally minimal triangulations of all lens spaces L p, q .
UR - http://www.scopus.com/inward/record.url?scp=67650799185&partnerID=8YFLogxK
U2 - 10.4310/jdg/1242134369
DO - 10.4310/jdg/1242134369
M3 - Article
AN - SCOPUS:67650799185
VL - 82
SP - 101
EP - 114
JO - Journal of Differential Geometry
JF - Journal of Differential Geometry
SN - 0022-040X
IS - 1
ER -
ID: 40113770