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[MathJax on]
A short HAP tutorial
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A more comprehensive tutorial is available here
and
A related book is available here
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The
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Graham Ellis
Contents
1
Simplicial complexes & CW complexes
1.1
The Klein bottle as a simplicial complex
1.2
Other simplicial surfaces
1.3
The Quillen complex
1.4
The Quillen complex as a reduced CW-complex
1.5
Simple homotopy equivalences
1.6
Cellular simplifications preserving homeomorphism type
1.7
Constructing a CW-structure on a knot complement
1.8
Constructing a regular CW-complex from its face lattice
1.9
Cup products
1.10
Cohomology Rings
1.11
Intersection forms of
4
-manifolds
1.12
CW maps and induced homomorphisms
1.13
Constructing a simplicial complex from a regular CW-complex
1.14
Equivariant CW complexes
1.15
Orbifolds and classifying spaces
2
Cubical complexes & permutahedral complexes
2.1
Cubical complexes
2.2
Permutahedral complexes
2.3
Constructing pure cubical and permutahedral complexes
2.4
Computations in dynamical systems
3
Covering spaces
3.1
Cellular chains on the universal cover
3.2
Spun knots and the Satoh tube map
3.3
Cohomology with local coefficients
3.4
Distinguishing between two non-homeomorphic homotopy equivalent spaces
3.5
Second homotopy groups of spaces with finite fundamental group
3.6
Third homotopy groups of simply connected spaces
3.6-1
First example
3.6-2
Second example
3.7
Computing the second homotopy group of a space with infinite fundamental group
4
Topological data analysis
4.1
Persistent homology
4.1-1
Background to the data
4.2
Mapper clustering
4.2-1
Background to the data
4.3
Digital image analysis
4.3-1
Background to the data
4.4
Random simplicial complexes
5
Group theoretic computations
5.1
Third homotopy group of a supsension of an Eilenberg-MacLane space
5.2
Representations of knot quandles
5.3
Aspherical
2
-complexes
5.4
Bogomolov multiplier
5.5
Second group cohomology and group extensions
5.6
Second group cohomology and cocyclic Hadamard matrices
5.7
Third group cohomology and homotopy
2
-types
6
Cohomology of groups
6.1
Finite groups
6.2
Nilpotent groups
6.3
Crystallographic groups
6.4
Arithmetic groups
6.5
Artin groups
6.6
Graphs of groups
6.7
Cohomology with coefficients in a module
6.8
Exact cohomology coefficient sequence
7
Cohomology operations
7.1
Steenrod operations on the classifying space of a finite
2
-group
7.2
Steenrod operations on the classifying space of a finite
p
-group
8
Bredon homology
8.1
Davis complex
8.2
Arithmetic groups
8.3
Crystallographic groups
9
Simplicial groups
9.1
Crossed modules
9.2
Eilenberg-MacLane spaces as simplicial groups (not recommended)
9.3
Eilenberg-MacLane spaces as simplicial free abelian groups (recommended)
9.4
Elementary theoretical information on
H^∗(K(π,n), Z)
9.5
The first three non-trivial homotopy groups of spheres
9.6
The first two non-trivial homotopy groups of the suspension and double suspension of a
K(G,1)
9.7
Postnikov towers and
π_5(S^3)
9.8
Towards
π_4(Σ K(G,1))
9.9
Enumerating homotopy 2-types
9.10
Identifying cat
^1
-groups of low order
9.11
Identifying crossed modules of low order
10
Congruence Subgroups, Cuspidal Cohomology and Hecke Operators
10.1
Eichler-Shimura isomorphism
10.2
Generators for
SL_2( Z)
and the cubic tree
10.3
One-dimensional fundamental domains and generators for congruence subgroups
10.4
Cohomology of congruence subgroups
10.5
Cuspidal cohomology
10.6
Hecke operators
10.7
Reconstructing modular forms from cohomology computations
10.8
The Picard group
10.9
Bianchi groups
10.10
Some other infinite matrix groups
10.11
Ideals and finite quotient groups
10.12
Congruence subgroups for ideals
10.13
First homology
11
Parallel computation
11.1
An embarassingly parallel computation
11.2
An non-embarassingly parallel computation
12
Regular CW-structure on knots
12.1
Knot complements in the 3-ball
12.2
Tubular neighbourhoods
12.3
Knotted surface complements in the 4-ball
References
Index
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