  
  
                              [1XA short HAP tutorial[101X
  
  
                [1X(A more comprehensive tutorial is available here
      ([7X../../www/SideLinks/About/aboutContents.html[107X) and A related book is
                                 available here
                                       (
  https://global.oup.com/academic/product/an-invitation-to-computational-homotopy-9780198832980
            ) and The [12XHAP[112X home page is here ([7X../../www/index.html[107X))[101X
  
  
                                  Graham Ellis
  
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (HAP commands)[101X
  
  1 [33X[0;0YSimplicial complexes & CW complexes[133X
    1.1 [33X[0;0YThe Klein bottle as a simplicial complex[133X
    1.2 [33X[0;0YThe Quillen complex[133X
    1.3 [33X[0;0YThe Quillen complex as a reduced CW-complex[133X
    1.4 [33X[0;0YConstructing a regular CW-complex from its face lattice[133X
    1.5 [33X[0;0YCup products[133X
    1.6 [33X[0;0YCW maps and induced homomorphisms[133X
  2 [33X[0;0YCubical complexes & permutahedral complexes[133X
    2.1 [33X[0;0YCubical complexes[133X
    2.2 [33X[0;0YPermutahedral complexes[133X
    2.3 [33X[0;0YConstructing pure cubical and permutahedral complexes[133X
    2.4 [33X[0;0YComputations in dynamical systems[133X
  3 [33X[0;0YCovering spaces[133X
    3.1 [33X[0;0YCellular chains on the universal cover[133X
    3.2 [33X[0;0YSpun knots and the Satoh tube map[133X
    3.3 [33X[0;0YCohomology with local coefficients[133X
    3.4 [33X[0;0YDistinguishing between two non-homeomorphic homotopy equivalent spaces[133X
    3.5 [33X[0;0YSecond homotopy groups of spaces with finite fundamental group[133X
    3.6 [33X[0;0YThird homotopy groups of simply connected spaces[133X
      3.6-1 [33X[0;0YFirst example[133X
      3.6-2 [33X[0;0YSecond example[133X
  4 [33X[0;0YTopological data analysis[133X
    4.1 [33X[0;0YPersistent homology[133X
      4.1-1 [33X[0;0YBackground to the data[133X
    4.2 [33X[0;0YMapper clustering[133X
      4.2-1 [33X[0;0YBackground to the data[133X
    4.3 [33X[0;0YDigital image analysis[133X
      4.3-1 [33X[0;0YBackground to the data[133X
  5 [33X[0;0YGroup theoretic computations[133X
    5.1 [33X[0;0YThird homotopy group of a supsension of an Eilenberg-MacLane space[133X
    5.2 [33X[0;0YRepresentations of knot quandles[133X
    5.3 [33X[0;0YAspherical [22X2[122X-complexes[133X
    5.4 [33X[0;0YBogomolov multiplier[133X
  6 [33X[0;0YCohomology of groups[133X
    6.1 [33X[0;0YFinite groups[133X
    6.2 [33X[0;0YNilpotent groups[133X
    6.3 [33X[0;0YCrystallographic groups[133X
    6.4 [33X[0;0YArithmetic groups[133X
    6.5 [33X[0;0YArtin groups[133X
    6.6 [33X[0;0YGraphs of groups[133X
  7 [33X[0;0YCohomology operations[133X
    7.1 [33X[0;0YSteenrod operations on the classifying space of a finite [22X2[122X-group[133X
    7.2 [33X[0;0YSteenrod operations on the classifying space of a finite [22Xp[122X-group[133X
  8 [33X[0;0YBredon homology[133X
    8.1 [33X[0;0YDavis complex[133X
    8.2 [33X[0;0YArithmetic groups[133X
    8.3 [33X[0;0YCrystallographic groups[133X
  9 [33X[0;0YSimplicial groups[133X
    9.1 [33X[0;0YCrossed modules[133X
    9.2 [33X[0;0YEilenberg-MacLane spaces[133X
  10 [33X[0;0YCongruence Subgroups, Cuspidal Cohomology and Hecke Operators[133X
    10.1 [33X[0;0YEichler-Shimura isomorphism[133X
    10.2 [33X[0;0YGenerators for [22XSL_2( Z)[122X and the cubic tree[133X
    10.3 [33X[0;0YOne-dimensional fundamental domains and generators for congruence
    subgroups[133X
    10.4 [33X[0;0YCohomology of congruence subgroups[133X
    10.5 [33X[0;0YCuspidal cohomology[133X
    10.6 [33X[0;0YHecke operators[133X
    10.7 [33X[0;0YReconstructing modular forms from cohomology computations[133X
    10.8 [33X[0;0YThe Picard group[133X
    10.9 [33X[0;0YBianchi groups[133X
    10.10 [33X[0;0YSome other infinite matrix groups[133X
    10.11 [33X[0;0YIdeals and finite quotient groups[133X
    10.12 [33X[0;0YCongruence subgroups for ideals[133X
    10.13 [33X[0;0YFirst homology[133X
  11 [33X[0;0YParallel computation[133X
    11.1 [33X[0;0YAn embarassingly parallel computation[133X
  
  
  [32X
