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[MathJax on]
A short HAP tutorial
(
A more comprehensive tutorial is available here
and
A related book is available here
and
The
HAP
home page is here
)
Graham Ellis
Contents
1
Simplicial complexes & CW complexes
1.1
The Klein bottle as a simplicial complex
1.2
The Quillen complex
1.3
The Quillen complex as a reduced CW-complex
1.4
Constructing a regular CW-complex from its face lattice
1.5
Cup products
1.6
CW maps and induced homomorphisms
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
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
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
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
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
10
Parallel computation
10.1
An embarassingly parallel computation
References
Index
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