Generalized Mom-structures and ideal triangulations of $3$–manifolds with nonspherical boundary
| Autor: | Ekaterina Pervova |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Ideal (set theory)
57M20 57N10 (primary) 57M15 57M50 (secondary) Mathematical analysis Boundary (topology) Geometric Topology (math.GT) triangulation Mathematics::Geometric Topology 57M50 Mathematics - Geometric Topology 57N10 57M20 57M15 FOS: Mathematics $3$–manifold Geometry and Topology Mom-structure Mathematics |
| Zdroj: | Algebr. Geom. Topol. 12, no. 1 (2012), 235-265 |
| Popis: | The so-called Mom-structures on hyperbolic cusped 3-manifolds without boundary were introduced by Gabai, Meyerhoff, and Milley, and used by them to identify the smallest closed hyperbolic manifold. In this work we extend the notion of a Mom-structure to include the case of 3-manifolds with non-empty boundary that does not have spherical components. We then describe a certain relation between such generalized Mom-structures, called protoMom-structures, internal on a fixed 3-manifold N, and ideal triangulations of N; in addition, in the case of non-closed hyperbolic manifolds without annular cusps, we describe how an internal geometric protoMom-structure can be constructed starting from Epstein-Penner or Kojima decomposition. Finally, we exhibit a set of combinatorial moves that relate any two internal protoMom-structures on a fixed N to each other. Comment: 38 pages, 19 figues; exposition style changed, particularly in Section 2.2; minor content changes in Section 2.1 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|