\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}{The Quillen complex}{chapter.1}% 3
\BOOKMARK [1][-]{section.1.3}{The Quillen complex as a reduced CW-complex}{chapter.1}% 4
\BOOKMARK [1][-]{section.1.4}{Constructing a regular CW-complex from its face lattice}{chapter.1}% 5
\BOOKMARK [1][-]{section.1.5}{Cup products}{chapter.1}% 6
\BOOKMARK [1][-]{section.1.6}{CW maps and induced homomorphisms}{chapter.1}% 7
\BOOKMARK [0][-]{chapter.2}{Cubical complexes \046 permutahedral complexes}{}% 8
\BOOKMARK [1][-]{section.2.1}{Cubical complexes}{chapter.2}% 9
\BOOKMARK [1][-]{section.2.2}{Permutahedral complexes}{chapter.2}% 10
\BOOKMARK [1][-]{section.2.3}{Constructing pure cubical and permutahedral complexes}{chapter.2}% 11
\BOOKMARK [1][-]{section.2.4}{Computations in dynamical systems}{chapter.2}% 12
\BOOKMARK [0][-]{chapter.3}{Covering spaces}{}% 13
\BOOKMARK [1][-]{section.3.1}{Cellular chains on the universal cover}{chapter.3}% 14
\BOOKMARK [1][-]{section.3.2}{Spun knots and the Satoh tube map}{chapter.3}% 15
\BOOKMARK [1][-]{section.3.3}{Cohomology with local coefficients}{chapter.3}% 16
\BOOKMARK [1][-]{section.3.4}{Distinguishing between two non-homeomorphic homotopy equivalent spaces}{chapter.3}% 17
\BOOKMARK [1][-]{section.3.5}{ Second homotopy groups of spaces with finite fundamental group}{chapter.3}% 18
\BOOKMARK [1][-]{section.3.6}{Third homotopy groups of simply connected spaces}{chapter.3}% 19
\BOOKMARK [0][-]{chapter.4}{Topological data analysis}{}% 20
\BOOKMARK [1][-]{section.4.1}{Persistent homology }{chapter.4}% 21
\BOOKMARK [1][-]{section.4.2}{Mapper clustering}{chapter.4}% 22
\BOOKMARK [1][-]{section.4.3}{Digital image analysis}{chapter.4}% 23
\BOOKMARK [0][-]{chapter.5}{Group theoretic computations}{}% 24
\BOOKMARK [1][-]{section.5.1}{Third homotopy group of a supsension of an Eilenberg-MacLane space }{chapter.5}% 25
\BOOKMARK [1][-]{section.5.2}{Representations of knot quandles}{chapter.5}% 26
\BOOKMARK [1][-]{section.5.3}{Aspherical 2-complexes}{chapter.5}% 27
\BOOKMARK [1][-]{section.5.4}{Bogomolov multiplier}{chapter.5}% 28
\BOOKMARK [0][-]{chapter.6}{Cohomology of groups}{}% 29
\BOOKMARK [1][-]{section.6.1}{Finite groups }{chapter.6}% 30
\BOOKMARK [1][-]{section.6.2}{Nilpotent groups}{chapter.6}% 31
\BOOKMARK [1][-]{section.6.3}{Crystallographic groups}{chapter.6}% 32
\BOOKMARK [1][-]{section.6.4}{Arithmetic groups}{chapter.6}% 33
\BOOKMARK [1][-]{section.6.5}{Artin groups}{chapter.6}% 34
\BOOKMARK [1][-]{section.6.6}{Graphs of groups}{chapter.6}% 35
\BOOKMARK [0][-]{chapter.7}{Cohomology operations}{}% 36
\BOOKMARK [1][-]{section.7.1}{Steenrod operations on the classifying space of a finite 2-group}{chapter.7}% 37
\BOOKMARK [1][-]{section.7.2}{Steenrod operations on the classifying space of a finite p-group}{chapter.7}% 38
\BOOKMARK [0][-]{chapter.8}{Bredon homology}{}% 39
\BOOKMARK [1][-]{section.8.1}{Davis complex}{chapter.8}% 40
\BOOKMARK [1][-]{section.8.2}{Arithmetic groups}{chapter.8}% 41
\BOOKMARK [1][-]{section.8.3}{Crystallographic groups}{chapter.8}% 42
\BOOKMARK [0][-]{chapter.9}{Simplicial groups}{}% 43
\BOOKMARK [1][-]{section.9.1}{Crossed modules}{chapter.9}% 44
\BOOKMARK [1][-]{section.9.2}{Eilenberg-MacLane spaces}{chapter.9}% 45
\BOOKMARK [0][-]{chapter.10}{Congruence Subgroups, Cuspidal Cohomology and Hecke Operators}{}% 46
\BOOKMARK [1][-]{section.10.1}{Eichler-Shimura isomorphism}{chapter.10}% 47
\BOOKMARK [1][-]{section.10.2}{Generators for SL2\(Z\) and the cubic tree}{chapter.10}% 48
\BOOKMARK [1][-]{section.10.3}{One-dimensional fundamental domains and generators for congruence subgroups}{chapter.10}% 49
\BOOKMARK [1][-]{section.10.4}{Cohomology of congruence subgroups}{chapter.10}% 50
\BOOKMARK [1][-]{section.10.5}{Cuspidal cohomology}{chapter.10}% 51
\BOOKMARK [1][-]{section.10.6}{Hecke operators}{chapter.10}% 52
\BOOKMARK [1][-]{section.10.7}{Reconstructing modular forms from cohomology computations}{chapter.10}% 53
\BOOKMARK [1][-]{section.10.8}{The Picard group}{chapter.10}% 54
\BOOKMARK [1][-]{section.10.9}{Bianchi groups}{chapter.10}% 55
\BOOKMARK [1][-]{section.10.10}{Some other infinite matrix groups}{chapter.10}% 56
\BOOKMARK [1][-]{section.10.11}{Ideals and finite quotient groups}{chapter.10}% 57
\BOOKMARK [1][-]{section.10.12}{Congruence subgroups for ideals}{chapter.10}% 58
\BOOKMARK [1][-]{section.10.13}{First homology}{chapter.10}% 59
\BOOKMARK [0][-]{chapter.11}{Parallel computation}{}% 60
\BOOKMARK [1][-]{section.11.1}{An embarassingly parallel computation}{chapter.11}% 61
\BOOKMARK [0][-]{chapter*.2}{References}{}% 62
