HAP is a homological algebra library for use with the GAP computer algebra system, and is still under development. Its initial focus is on computations related to the cohomology of groups. Both finite and infinite groups are handled, with emphasis on integral coefficients. Recent additions include some functions for computing homology of crossed modules and simplicial groups, and also some functions for handling simplicial complexes, cubical complexes and regular CW-complexes in the context of topological data analysis.


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  1. Hoshi, Akinari; Kang, Ming-chang; Yamasaki, Aiichi: Degree three unramified cohomology groups and Noether’s problem for groups of order 243 (2020)
  2. Szymik, Markus: The third Milgram-Priddy class lifts (2020)
  3. Bui, Anh Tuan; Rahm, Alexander D.; Wendt, Matthias: The Farrell-Tate and Bredon homology for (\operatornamePSL_4(\mathbbZ)) via cell subdivisions (2019)
  4. Ellis, Graham: An invitation to computational homotopy (2019)
  5. Hatui, Sumana: Characterization of finite (p)-groups by their Schur multiplier (2018)
  6. Carr, Hamish (ed.); Garth, Christoph (ed.); Weinkauf, Tino (ed.): Topological methods in data analysis and visualization IV. Theory, algorithms, and applications. Selected papers based on the presentations at the TopoInVis workshop, Annweiler, Germany, 2015 (2017)
  7. Hatui, Sumana: Finite (p)-groups having Schur multiplier of maximum order (2017)
  8. Hoshi, Akinari; Yamasaki, Aiichi: Rationality problem for algebraic tori (2017)
  9. Schauenburg, Peter: Erratum to: “A higher Frobenius-Schur indicator formula for group-theoretical fusion categories” (2017)
  10. Schönnenbeck, Sebastian: Resolutions for unit groups of orders (2017)
  11. Bui, A. T.; Ellis, Graham: Computing Bredon homology of groups (2016)
  12. Ellis, Graham: Cohomological periodicities of crystallographic groups. (2016)
  13. Lambe, Larry A.: An algebraic study of the Klein bottle (2016)
  14. Odabaş, A.; Uslu, E. Ö.; Ilgaz, E.: Isoclinism of crossed modules (2016)
  15. Brendel, Piotr; Dłotko, Paweł; Ellis, Graham; Juda, Mateusz; Mrozek, Marian: Computing fundamental groups from point clouds (2015)
  16. Lutowski, Rafał; Putrycz, Bartosz: Spin structures on flat manifolds (2015)
  17. Rai, Pradeep K.; Yadav, Manoj K.: On (\mathrm\textШ)-rigidity of groups of order (p^6). (2015)
  18. Bui, Anh Tuan; Ellis, Graham: The homology of (SL_2(\mathbbZ[1/m])) for small (m). (2014)
  19. Ellis, Graham; Hegarty, Fintan: Computational homotopy of finite regular CW-spaces (2014)
  20. Jezernik, Urban; Moravec, Primož: Bogomolov multipliers of groups of order 128 (2014)

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