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Richter-Gebert J. — Realization Spaces of Polytopes, Vol. 164
Richter-Gebert J. — Realization Spaces of Polytopes, Vol. 164

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Название: Realization Spaces of Polytopes, Vol. 164

Автор: Richter-Gebert J.

Аннотация:

The book collects results about realization spaces of polytopes. It gives a presentation of the author's "Universality Theorem for 4-polytopes". It is a comprehensive survey of the important results that have been obtained in that direction. The approaches chosen are direct and very geometric in nature. The book is addressed to researchers and to graduate students. The former will find a comprehensive source for the above mentioned results. The latter will find a readable introduction to the field. The reader is assumed to be familiar with basic concepts of linear algebra.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 204

Добавлена в каталог: 04.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\sigma$-construction      5
2-sphere      4
3-connected      3 117
3-Polytope      3
3-polytopes      117
3-sphere      5 84
4-polytope      6
ab-manifold      154
Adapter      51
Adapter, generalized      149
Addition      6 10 41 59 113
Admissible basis      3
Admissible hyperplane      15
Admissible projective transformation      15 18 30
Affine basis      19 24
Affine configuration      15 33
Affine dimension      15
Affine equivalence      18
Affine functional      13
Affine hull      14
Affine transformation      13 18
Affinely independent      2
Algebra      1
Algebraic complexity      21
Algebraic geometry      2
Algebraic numbers      5 6 78 95
algorithmic complexity      77 78
Algorithmic Steinitz problem      77
Alternative construction      82 90 151
Altshuler, Amos      174
Andreev, E.M.      3 117
Arbitrarily prescribable      4—6 38 39 50 95
Associated cone      16
atomic      16
Balinski's theorem      117
Barnette, David W.      4 5 38 174
Basic building block      45
Basic building blocks      8
Basis      2
Basis of a diagram      88
Basis, admissible      3
Basis, Affine      19 24
Bokowski — Ewald — Kleinschmidt polytope      5 38 173
Bokowski, Juergen      5 38 173 174
Brueckner, Max      174
Building block, basic      45
Building block, composed      45
Cairns' smoothing theory      2 174
cell      120
Chirotope      112 163
Circle packing theorem      3 117
Cluster      100 103
Coatomic      16
Cocircuit      34 163
Cocircuit, external      34
Codimension      4
Combinatorial polytope      15 17 29
Combinatorial sphere      4
Combinatorial structure      16
Combinatorial type      1 16
Combinatorics      1
Complexity, algebraic      21
Complexity, algorithmic      77 78
Composed building block      45
Computation frame      42
Computation frame, normal      43
Computation frame, standardized      44
Computation, geometric      6
Cone      15
Cone, associated      16
Configuration, affine      15 33
Configuration, linear      15
conic      151
Connected sum      8 29
Connector      10 47
Construction diagram      45 58 61 63 66
Constructions      7 28
Contractible      4
Contraction      84
Convex hull      1 14
Convex polytope      15
Coordinates, homogeneous      15
Corollaries      6 95
Counterexamples      4
Covector      163
Crapo, Henry      133
Cross product      13
Cross ratio      43
cube      2 17 18 20 176
CYCLE      118
d-polytope      1 16
Defining equations      8 21
Dehomogenization      15
Deletion      84 118
Diagram      87 88
Differential topology      2
DIMENSION      1 4
Dimension of a cone      15
Dimension of a polytopal complex      87
Dimension of a polytope      15
Dimension, affine      15
Dimension, linear      15
Doubly exponential      6 81 95 175
Duality      24
Edge graph      3 120
Edge length, rational      176
Empty set      2
Equations, defining      21
Equations, polynomial      3 21
Equilibrium      123 133
Equivalence, affine      18
Equivalence, homotopy      3 5 6 23 95
Equivalence, Lawrence      36
Equivalence, linear      18
Equivalence, projective      18
Equivalence, rational      22 97
Equivalence, stable      5 22 71 97
Euclidean length      13
Euclidean scale      43
Eulers's Theorem      121
Ewald, Guenter      5 38 173
Existential Theory of the Reals      5 6 77 95
Exponential, doubly      6 81 95 175
Exponential, singly      4 140 175
External cocircuit      34
Extreme points      2
Face      1 16
Face lattice      1 16
Face lattice, polar      25
Facet      16
Fan      87 89
Fary, Istvan      119
Fibration, trivial      21
Finite lattice      2
Flag transitive      1
Flat, necessarily      8 31
Forbidden minors      6 84 95 151
Forgetful transmitter      10 48 81
Frame computation      42
Frame information      45
Functional, affine      13
Functional, linear      13
Gale diagram      5
Gale duality      4 5
Generalized adapter      149
Geometric computation      6
Geometry      1
Geometry, algebraic      2
Geometry, real discrete      2
Gluing      29
Goodman, Jacob E.      81 175
Graph      3 117 118
Graph, planar      119
Graph, stress      122
Gruenbaum, Branko      4 13 174
Guenzel, Harald      2 97 101
Harmonic polytope      56
Harmonic set      55
Homogeneous coordinates      15
Homogenization      15
Homotopy equivalence      3 5 6 23 95
Homotopy type      21
Hopcroft, John E.      133
Hull, affine      14
Hull, convex      1 14
Hull, linear      14
Hull, positive      14
Hypercube      27
Hyperplane, admissible      15
Incidence structures      6
Inequalities, non-strict      21
Inequalities, polynomial      3 21
Information frame      45
Information line      113
Inner cell      88
Integral vertex coordinates      4
Interior edges      123
Interior vertices      123
k-face      16
Kahn, Peter J.      133
Kleinschmidt polytope      5 38
Kleinschmidt, Peter      4 5 38 173
Koebe, Paul      3 117
Labelings      14
Lattice, finite      2
Lawrence construction      34
Lawrence equivalence      36
Lawrence extension      7 32 33
Lawrence polytope      7 33
Lawrence, Jim      33
Length, euclidean      13
Lifting      117 133
Linear algebra      13
Linear configuration      15
Linear dimension      15
Linear equivalence      18
Linear functional      13
Linear hull      14
Linear transformation      13
Mani, Peter      4
Maxwell, James C.      133
McMullen, Peter      133
Menger's Theorem      121
Minors, forbidden      6 84 95 151
Mneev's, Universality Theorem      5 173
Mneev, Nicolai E.      5 97 173
Moduli spaces      2
Multiplication      6 10 41 62 113
Necessarily flat      8 31
Net      92
Non-polytopal sphere      5 84
Non-prescribable      5 6 38 39 50 95
Non-rational points      3
Non-rational polytope      5 6 78 95 174
Non-Steinitz Theorem      84 151
Non-strict inequalities      21
Nonlinear optimization      2
Normal computation frame      43
Normal form      41 68
NP-hard      5 6 77 95
Octagon      55 78
Onn, Shmuel      4 81
Optimization, nonlinear      2
Oriented matroid      5 7 32 112 163
Partially ordered set      16
Pascal's theorem      39
Path      118
Peripheral edges      123
Peripheral vertices      123
Perles, Micha A.      5 174
PL-sphere      17
Planar      3 117
Planar graph      119
Planet      165
Platonic solids      1
Point configuration      14 32
Points, extreme      2
Points, non-rational      3
Points, rational      4
Polar face lattice      25
Polar polytope      25
Polarity      24
Pollack, Richard      81 175
Polygon      42
Polynomial equations      3 21
Polynomial inequalities      3 21
Polytopal      16
Polytopal complex      87
Polytopal sphere      4
Polytopal tools      7
Polytope      1 15
Polytope for addition      59
Polytope for multiplication      62
Polytope, codimension four      5
Polytope, combinatorial      15 17 29
Polytope, convex      15
Polytope, four-dimensional      6
Polytope, harmonic      56
Polytope, high-dimensional      4
Polytope, non-rational      5 6 78 95 174
Polytope, polar      25
Polytope, switch      107
Polytope, three-dimensional      3 117
POSET      16
Positive hull      14
Prescribable      4—6 38 39 50 95
Primary semialgebraic set      3 8 21 41
prism      8 28 31 45
Problems      173
Product, cross      13
Product, scalar      13
Projection, stable      21 97
Projective equivalence      18
Projective plane      6
Projective scale      10 42 43 113
Projective space      93
Projective transformation      31
Projective transformation, admissible      15 18 30
Pyramid      8 28 31 45
Quadratic Cone      151
Quadrilateral ratio      100
Quadrilateral set      99 106
Ratio, cross      43
Ratio, quadrilateral      100
Rational edge length      176
Rational points      4
Rationed equivalence      22 97
Real discrete geometry      2
Realizability problem for 3-diagrams      95
Realizability problem for 4-polytopes      6
Realizability problem for codimension 4-polytopes      5
Realization      19
Realization space      1 3 20
Realization space of a 3-polytope      4 144
Realization space of a 4-polytope      6
Realization space of a codimension 4-polytope      5
Realization space of a connected sum      32
Realization space of a diagram      88
Realization space of a fan      89
Realization space of a Lawrence extension      36
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