Goto Chapter:
Top
1
2
3
4
5
6
7
8
9
10
11
12
13
Bib
Ind
[Top of Book]
[Contents]
[Next Chapter]
[MathJax off]
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
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 by attaching cells
1.9
Constructing a regular CW-complex from its face lattice
1.10
Cup products
1.11
Cohomology Rings
1.12
Intersection forms of
\(4\)
-manifolds
1.13
CW maps and induced homomorphisms
1.14
Constructing a simplicial complex from a regular CW-complex
1.15
Equivariant CW complexes
1.16
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: Whitehead's certain exact sequence
3.6-2
Second example: the Hopf invariant
3.7
Computing the second homotopy group of a space with infinite fundamental group
4
Three Manifolds
4.1
Dehn Surgery
4.2
Dijkgraaf-Witten Invariant
4.3
Cohomology rings
4.4
Linking Form
5
Topological data analysis
5.1
Persistent homology
5.1-1
Background to the data
5.2
Mapper clustering
5.2-1
Background to the data
5.3
Digital image analysis
5.3-1
Background to the data
5.4
Random simplicial complexes
6
Group theoretic computations
6.1
Third homotopy group of a supsension of an Eilenberg-MacLane space
6.2
Representations of knot quandles
6.3
Identifying knots
6.4
Aspherical
\(2\)
-complexes
6.5
Bogomolov multiplier
6.6
Second group cohomology and group extensions
6.7
Second group cohomology and cocyclic Hadamard matrices
6.8
Third group cohomology and homotopy
\(2\)
-types
7
Cohomology of groups
7.1
Finite groups
7.2
Nilpotent groups
7.3
Crystallographic groups
7.4
Arithmetic groups
7.5
Artin groups
7.6
Graphs of groups
7.7
Cohomology with coefficients in a module
7.8
Exact cohomology coefficient sequence
7.9
Cohomology rings of finite fundamental groups of 3-manifolds
8
Cohomology operations
8.1
Steenrod operations on the classifying space of a finite
\(2\)
-group
8.2
Steenrod operations on the classifying space of a finite
\(p\)
-group
9
Bredon homology
9.1
Davis complex
9.2
Arithmetic groups
9.3
Crystallographic groups
10
Simplicial groups
10.1
Crossed modules
10.2
Eilenberg-MacLane spaces as simplicial groups (not recommended)
10.3
Eilenberg-MacLane spaces as simplicial free abelian groups (recommended)
10.4
Elementary theoretical information on
\(H^\ast(K(\pi,n),\mathbb Z)\)
10.5
The first three non-trivial homotopy groups of spheres
10.6
The first two non-trivial homotopy groups of the suspension and double suspension of a
\(K(G,1)\)
10.7
Postnikov towers and
\(\pi_5(S^3)\)
10.8
Towards
\(\pi_4(\Sigma K(G,1))\)
10.9
Enumerating homotopy 2-types
10.10
Identifying cat
\(^1\)
-groups of low order
10.11
Identifying crossed modules of low order
11
Congruence Subgroups, Cuspidal Cohomology and Hecke Operators
11.1
Eichler-Shimura isomorphism
11.2
Generators for
\(SL_2(\mathbb Z)\)
and the cubic tree
11.3
One-dimensional fundamental domains and generators for congruence subgroups
11.4
Cohomology of congruence subgroups
11.4-1
Cohomology with rational coefficients
11.5
Cuspidal cohomology
11.6
Hecke operators
11.7
Reconstructing modular forms from cohomology computations
11.8
The Picard group
11.9
Bianchi groups
11.10
Some other infinite matrix groups
11.11
Ideals and finite quotient groups
11.12
Congruence subgroups for ideals
11.13
First homology
12
Parallel computation
12.1
An embarassingly parallel computation
12.2
An non-embarassingly parallel computation
13
Regular CW-structure on knots
13.1
Knot complements in the 3-ball
13.2
Tubular neighbourhoods
13.3
Knotted surface complements in the 4-ball
References
Index
[Top of Book]
[Contents]
[Next Chapter]
Goto Chapter:
Top
1
2
3
4
5
6
7
8
9
10
11
12
13
Bib
Ind
generated by
GAPDoc2HTML