=================================================================  ===================================  ===================================
:Author: Clément Maria                                             :Introduced in: GUDHI 2.0.0          :Copyright: GPL v3
=================================================================  ===================================  ===================================

+-----------------------------------------------------------------+-----------------------------------------------------------------------+
| .. figure::                                                     | The theory of homology consists in attaching to a topological space   |
|      ../../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  |
|                                                                 | 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    |
|      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:journals/corr/abs-1208-5018` 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`                                 |
+-----------------------------------------------------------------+-----------------------------------------------------------------------+