算法拓扑学及三维流形的分类(第二版)(英文影印版)

.2.1.1almost simple polyhedra
2.1.2definition and estimation of the complexity
2.2properties of complexity
2.2.1converting almost simple spines into special ones
2.2.2the finiteness property
2.2.3the additivity property
2.3closed manifolds of small complexity
2.3.1enumeration procedure
2.3.2simplification moves
2.3.3manifolds of complexity _[ 6
2.4graph manifolds of waldhausen
2.4.1properties of graph manifolds
2.4.2manifolds of complexity [8
2.5hyperbolic manifolds
2.5.1hyperbolic manifolds of complexity 9
2.6lower bounds of the complexity
2.6.1logarithmic estimates
2.6.2complexity of hyperbolic 3-manifolds
2.6.3manifolds having special spines with one 2-cell
haken theory of normal surfaces
3.1basic notions and haken's scheme
3.2theory of normal curves
3.2.1normal curves and normal equations
3.2.2fundamental solutions and fundamental curves
3.2.3geometric summation
3.2.4an alternative approach to the theory of normal
curves
3.3normal surfaces in 3-manifolds
3.3.1incompressible surfaces
3.3.2normal surfaces in 3-manifolds with boundary pattern
3.3.3normalization procedure
3.3.4fundamental surfaces
3.3.5geometric summation
3.4normal surfaces in handle decompositions
applications of the theory of normal surfaces
4.1examples of algorithms based on haken's theory
4.1.1recognition of splittable links
4.1.2getting rid of clean disc patches
4.1.3recognizing the unknot and calculating the genus of a circle in the boundary of a 3-manifold
4.1.4is m3 irreducible and boundary irreducible?
4.1.5is a proper surface incompressible and boundary incompressible?
4.1.6is m3 sufficiently large?
4.2cutting 3-manifolds along surfaces
4.2.1normal surfaces and spines
4.2.2triangulations vs. handle decompositions
5 algorithmic recognition of sa
5.1links in a 3-ball
5.1.1compressing discs and one-legged crowns
5.1.2thin position of links
5.2the rubinstein theorem
5.2.12-normal surfaces
5.2.2proof of the rubinstein theorem
5.2.3the algorithm
6 classification of haken 3-manifolds
6.1main theorem
6.2the waldhausen theorem
6.2.1deforming homotopy equivalences of surfaces
6.2.2deforming homotopy equivalences of 3-manifolds to homeomorphisms
6.3finiteness properties for surfaces
6.3.1two reformulations of the recognition theorem
6.3.2abstract extension moves
6.3.3first finiteness property and a toy form
of the second
6.3.4second finiteness property for simple 3-manifolds
6.4jaco-shalen-johannson decomposition
6.4.1improving isotopy that separates surfaces
6.4.2does m3 contain essential tori and annuli?
6.4.3different types of essential tori and annuli
6.4.4jsj-decomposition exists and is unique
6.4.5seifert and/-bundle chambers
6.4.6third finiteness property
6.5extension moves
6.5.1description of general extension moves
6.5.2structure of chambers
6.5.3special extension moves: easy case
6.5.4difficult case
6.5.5recognition of simple stallings manifolds with periodic monodromy
6.5.6recognition of simple stallings manifolds with nonperiodic monodromy
6.5.7recognition of quasi-stallings manifolds
6.5.8subdivision of solid tori
6.5.9proof of the recognition theorem73-manifold recognizer
7.1computer presentation of 3-manifolds
7.1.1cell complexes
7.1.23-manifolds as thickened spines
7.2simplifying manifolds and spines
7.2.1coordinate systems on toff
7.2.2reduction of cell structures
7.2.3collapses
7.2.4surgeries
7.2.5disc replacement moves
7.3labeled molecules
7.3.1what is a labeled molecule?
7.3.2creating a labeled molecule
7.3.3assembling seifert atoms
7.4the algorithm
7.5tabulation
7.5.1comments on the table
7.5.2hyperbolic manifolds up to complexity 12
7.5.3why the table contains no duplicates?
7.6other applications of the 3-manifold recognizer
7.6.1enumeration of heegaard diagrams of genus 2
7.6.23-manifolds represented by crystallizationswith _[ 32 vertices
7.6.3classification of crystallizations of genus 2
7.6.4recognition of knots and unknots
7.7two-step enumeration of 3-manifolds
7.7.1relative spines and relative complexity
7.7.2assembling
7.7.3modified enumeration of manifolds and spines
8the turaev-viro invariants
8.1the turaev viro invariants
8.1.1the construction
8.1.2turaev-viro type invariants of order r＜3
8.1.3construction and properties of the e-invariant
8.1.4turaev-viro invariants of order r ＞3
8.1.5computing turaev-viro invariants
8.1.6more on ε-invariant
8.23-manifolds having the same invariantsof turaev-viro type
aappendix
a.1 manifolds of complexity ~ 6
a.2 minimal spines of manifolds up to complexity 6
a.3 minimal spines of some manifolds of complexity 7
a.4 tables of thraev-viro invariants
references
index