.. table:: :widths: 30 40 30 +-----------------------------------------------------------------+-----------------------------------------------------------------------+-----------------------------------------------+ | .. figure:: | The theory of homology consists in attaching to a topological space | :Author: Clément Maria | | ../../doc/Persistent_cohomology/3DTorus_poch.png | a sequence of (homology) groups, capturing global topological | | | :figclass: align-center | features like connected components, holes, cavities, etc. Persistent | :Since: GUDHI 2.0.0 | | | homology studies the evolution -- birth, life and death -- of these | | | Rips Persistent Cohomology on a 3D | features when the topological space is changing. Consequently, the | :License: MIT | | Torus | theory is essentially composed of three elements: topological spaces, | | | | their homology groups and an evolution scheme. | | | | | | | | Computation of persistent cohomology using the algorithm of | | | | :cite:`DBLP:journals/dcg/SilvaMV11` and | | | | :cite:`DBLP:conf/compgeom/DeyFW14` and the Compressed | | | | Annotation Matrix implementation of | | | | :cite:`DBLP:conf/esa/BoissonnatDM13`. | | | | | | +-----------------------------------------------------------------+-----------------------------------------------------------------------+-----------------------------------------------+ | * :doc:`persistent_cohomology_user` | Please refer to each data structure that contains persistence | | | feature for reference: | | | | | | * :doc:`simplex_tree_ref` | | | * :doc:`cubical_complex_ref` | | | * :doc:`periodic_cubical_complex_ref` | +-----------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------+