\BOOKMARK [0][-]{chapter.1}{Simplicial complexes \046 CW complexes}{}% 1
\BOOKMARK [1][-]{section.1.1}{The Klein bottle as a simplicial complex}{chapter.1}% 2
\BOOKMARK [1][-]{section.1.2}{Other simplicial surfaces}{chapter.1}% 3
\BOOKMARK [1][-]{section.1.3}{The Quillen complex}{chapter.1}% 4
\BOOKMARK [1][-]{section.1.4}{The Quillen complex as a reduced CW-complex}{chapter.1}% 5
\BOOKMARK [1][-]{section.1.5}{Simple homotopy equivalences}{chapter.1}% 6
\BOOKMARK [1][-]{section.1.6}{Cellular simplifications preserving homeomorphism type}{chapter.1}% 7
\BOOKMARK [1][-]{section.1.7}{Constructing a CW-structure on a knot complement}{chapter.1}% 8
\BOOKMARK [1][-]{section.1.8}{Constructing a regular CW-complex from its face lattice}{chapter.1}% 9
\BOOKMARK [1][-]{section.1.9}{Cup products}{chapter.1}% 10
\BOOKMARK [1][-]{section.1.10}{Cohomology Rings}{chapter.1}% 11
\BOOKMARK [1][-]{section.1.11}{Intersection forms of 4-manifolds}{chapter.1}% 12
\BOOKMARK [1][-]{section.1.12}{CW maps and induced homomorphisms}{chapter.1}% 13
\BOOKMARK [1][-]{section.1.13}{Constructing a simplicial complex from a regular CW-complex}{chapter.1}% 14
\BOOKMARK [1][-]{section.1.14}{Equivariant CW complexes}{chapter.1}% 15
\BOOKMARK [1][-]{section.1.15}{Orbifolds and classifying spaces}{chapter.1}% 16
\BOOKMARK [0][-]{chapter.2}{Cubical complexes \046 permutahedral complexes}{}% 17
\BOOKMARK [1][-]{section.2.1}{Cubical complexes}{chapter.2}% 18
\BOOKMARK [1][-]{section.2.2}{Permutahedral complexes}{chapter.2}% 19
\BOOKMARK [1][-]{section.2.3}{Constructing pure cubical and permutahedral complexes}{chapter.2}% 20
\BOOKMARK [1][-]{section.2.4}{Computations in dynamical systems}{chapter.2}% 21
\BOOKMARK [0][-]{chapter.3}{Covering spaces}{}% 22
\BOOKMARK [1][-]{section.3.1}{Cellular chains on the universal cover}{chapter.3}% 23
\BOOKMARK [1][-]{section.3.2}{Spun knots and the Satoh tube map}{chapter.3}% 24
\BOOKMARK [1][-]{section.3.3}{Cohomology with local coefficients}{chapter.3}% 25
\BOOKMARK [1][-]{section.3.4}{Distinguishing between two non-homeomorphic homotopy equivalent spaces}{chapter.3}% 26
\BOOKMARK [1][-]{section.3.5}{ Second homotopy groups of spaces with finite fundamental group}{chapter.3}% 27
\BOOKMARK [1][-]{section.3.6}{Third homotopy groups of simply connected spaces}{chapter.3}% 28
\BOOKMARK [1][-]{section.3.7}{Computing the second homotopy group of a space with infinite fundamental group}{chapter.3}% 29
\BOOKMARK [0][-]{chapter.4}{Topological data analysis}{}% 30
\BOOKMARK [1][-]{section.4.1}{Persistent homology }{chapter.4}% 31
\BOOKMARK [1][-]{section.4.2}{Mapper clustering}{chapter.4}% 32
\BOOKMARK [1][-]{section.4.3}{Digital image analysis}{chapter.4}% 33
\BOOKMARK [1][-]{section.4.4}{Random simplicial complexes}{chapter.4}% 34
\BOOKMARK [0][-]{chapter.5}{Group theoretic computations}{}% 35
\BOOKMARK [1][-]{section.5.1}{Third homotopy group of a supsension of an Eilenberg-MacLane space }{chapter.5}% 36
\BOOKMARK [1][-]{section.5.2}{Representations of knot quandles}{chapter.5}% 37
\BOOKMARK [1][-]{section.5.3}{Aspherical 2-complexes}{chapter.5}% 38
\BOOKMARK [1][-]{section.5.4}{Bogomolov multiplier}{chapter.5}% 39
\BOOKMARK [1][-]{section.5.5}{Second group cohomology and group extensions}{chapter.5}% 40
\BOOKMARK [1][-]{section.5.6}{Second group cohomology and cocyclic Hadamard matrices}{chapter.5}% 41
\BOOKMARK [1][-]{section.5.7}{Third group cohomology and homotopy 2-types}{chapter.5}% 42
\BOOKMARK [0][-]{chapter.6}{Cohomology of groups}{}% 43
\BOOKMARK [1][-]{section.6.1}{Finite groups }{chapter.6}% 44
\BOOKMARK [1][-]{section.6.2}{Nilpotent groups}{chapter.6}% 45
\BOOKMARK [1][-]{section.6.3}{Crystallographic groups}{chapter.6}% 46
\BOOKMARK [1][-]{section.6.4}{Arithmetic groups}{chapter.6}% 47
\BOOKMARK [1][-]{section.6.5}{Artin groups}{chapter.6}% 48
\BOOKMARK [1][-]{section.6.6}{Graphs of groups}{chapter.6}% 49
\BOOKMARK [1][-]{section.6.7}{Cohomology with coefficients in a module}{chapter.6}% 50
\BOOKMARK [1][-]{section.6.8}{Exact cohomology coefficient sequence}{chapter.6}% 51
\BOOKMARK [0][-]{chapter.7}{Cohomology operations}{}% 52
\BOOKMARK [1][-]{section.7.1}{Steenrod operations on the classifying space of a finite 2-group}{chapter.7}% 53
\BOOKMARK [1][-]{section.7.2}{Steenrod operations on the classifying space of a finite p-group}{chapter.7}% 54
\BOOKMARK [0][-]{chapter.8}{Bredon homology}{}% 55
\BOOKMARK [1][-]{section.8.1}{Davis complex}{chapter.8}% 56
\BOOKMARK [1][-]{section.8.2}{Arithmetic groups}{chapter.8}% 57
\BOOKMARK [1][-]{section.8.3}{Crystallographic groups}{chapter.8}% 58
\BOOKMARK [0][-]{chapter.9}{Simplicial groups}{}% 59
\BOOKMARK [1][-]{section.9.1}{Crossed modules}{chapter.9}% 60
\BOOKMARK [1][-]{section.9.2}{Eilenberg-MacLane spaces as simplicial groups \(not recommended\)}{chapter.9}% 61
\BOOKMARK [1][-]{section.9.3}{Eilenberg-MacLane spaces as simplicial free abelian groups \(recommended\)}{chapter.9}% 62
\BOOKMARK [1][-]{section.9.4}{Elementary theoretical information on H\(K\(,n\),Z\)}{chapter.9}% 63
\BOOKMARK [1][-]{section.9.5}{The first three non-trivial homotopy groups of spheres}{chapter.9}% 64
\BOOKMARK [1][-]{section.9.6}{The first two non-trivial homotopy groups of the suspension and double suspension of a K\(G,1\)}{chapter.9}% 65
\BOOKMARK [1][-]{section.9.7}{Postnikov towers and 5\(S3\) }{chapter.9}% 66
\BOOKMARK [1][-]{section.9.8}{Towards 4\(K\(G,1\)\) }{chapter.9}% 67
\BOOKMARK [1][-]{section.9.9}{Enumerating homotopy 2-types}{chapter.9}% 68
\BOOKMARK [1][-]{section.9.10}{Identifying cat1-groups of low order}{chapter.9}% 69
\BOOKMARK [1][-]{section.9.11}{Identifying crossed modules of low order}{chapter.9}% 70
\BOOKMARK [0][-]{chapter.10}{Congruence Subgroups, Cuspidal Cohomology and Hecke Operators}{}% 71
\BOOKMARK [1][-]{section.10.1}{Eichler-Shimura isomorphism}{chapter.10}% 72
\BOOKMARK [1][-]{section.10.2}{Generators for SL2\(Z\) and the cubic tree}{chapter.10}% 73
\BOOKMARK [1][-]{section.10.3}{One-dimensional fundamental domains and generators for congruence subgroups}{chapter.10}% 74
\BOOKMARK [1][-]{section.10.4}{Cohomology of congruence subgroups}{chapter.10}% 75
\BOOKMARK [1][-]{section.10.5}{Cuspidal cohomology}{chapter.10}% 76
\BOOKMARK [1][-]{section.10.6}{Hecke operators}{chapter.10}% 77
\BOOKMARK [1][-]{section.10.7}{Reconstructing modular forms from cohomology computations}{chapter.10}% 78
\BOOKMARK [1][-]{section.10.8}{The Picard group}{chapter.10}% 79
\BOOKMARK [1][-]{section.10.9}{Bianchi groups}{chapter.10}% 80
\BOOKMARK [1][-]{section.10.10}{Some other infinite matrix groups}{chapter.10}% 81
\BOOKMARK [1][-]{section.10.11}{Ideals and finite quotient groups}{chapter.10}% 82
\BOOKMARK [1][-]{section.10.12}{Congruence subgroups for ideals}{chapter.10}% 83
\BOOKMARK [1][-]{section.10.13}{First homology}{chapter.10}% 84
\BOOKMARK [0][-]{chapter.11}{Parallel computation}{}% 85
\BOOKMARK [1][-]{section.11.1}{An embarassingly parallel computation}{chapter.11}% 86
\BOOKMARK [1][-]{section.11.2}{An non-embarassingly parallel computation}{chapter.11}% 87
\BOOKMARK [0][-]{chapter.12}{Regular CW-structure on knots}{}% 88
\BOOKMARK [1][-]{section.12.1}{Knot complements in the 3-ball}{chapter.12}% 89
\BOOKMARK [1][-]{section.12.2}{Tubular neighbourhoods}{chapter.12}% 90
\BOOKMARK [1][-]{section.12.3}{Knotted surface complements in the 4-ball}{chapter.12}% 91
\BOOKMARK [0][-]{chapter*.2}{References}{}% 92
