Index
absolute homology group, 90
abstract simplicial complex, 53
Ackermann function, 8, 123, 145, 159
affine
combination, 51
hull, 51
independence, 51
Alexander
duality, 118
Duality Theorem, 120
alpha
complex, 69, 223
weighted, 69
shape, 69, 223
anti-cancellation, 208
ascending manifold, 131
augmentation map, 83
augmenting path, 192
balanced search tree, 144
barycenter, 54
barycentric
coordinate, 54, 135
subdivision, 54, 74, 119
basis of a topology, 5
Betti number, 81, 85
persistent, 151, 182
reduced, 83
bipartite graph, 191
birth, 151
bisector, 65
block, 168
chain, 111
Block Complex Lemma, 111
body centered cubic lattice, 146
Borromean rings, 24
bottleneck distance, 180
boundary, 80
group, 80
relative, 90
homomorphism, 80
map, 80, 95, 169
matrix, 86, 167
of a manifold, 28
of a simplex, 52
branch, 220
branch point, 42
Breadth-first Search, 35, 140, 193
Brouwer’s Fixed Point Theorem, 84
alug˘ areanu-White Formula, 17
cancellation, 208
Cauchy-Crofton Formula, 187
ˇ
Cech complex, 60
chain, 79
complex, 80, 95, 169
group, 80
relative, 90
map, 95
Classification Theorem for 2-manifolds, 29
closed
curve, 9, 186
simple, 9, 208
polygon, 10, 210
set, 6
star, 53
coboundary, 105
group, 105
map, 105
matrix, 107
cochain, 104
group, 105
cocycle, 105
group, 105
coface, 52
coherent triangulation, 68
cohomology group, 105
reduced, 105
cokernel, 93
collapse, 72
collapsible, 72, 75
collision, 157
coloring, 14, 24, 48
combination
affine, 51
convex, 20, 51
commutative square, 97
compact, 27
compatible ordering, 152, 167
complementary subcomplexes, 119
complex
abstract simplicial, 53
simplicial, 52
component, 4, 158
235
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