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===================================== ===================================== =====================================
:Author: Clément Maria :Introduced in: GUDHI 1.0.0 :Copyright: GPL v3
===================================== ===================================== =====================================
+---------------------------------------------+----------------------------------------------------------------------+
| .. image:: | The theory of homology consists in attaching to a topological space |
| img/3DTorus_poch.png | a sequence of (homology) groups, capturing global topological |
| | features like connected components, holes, cavities, etc. Persistent |
| | homology studies the evolution -- birth, life and death -- of these |
| | features when the topological space is changing. Consequently, the |
| | 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:`alpha_complex_ref` |
| | * :doc:`cubical_complex_ref` |
| | * :doc:`simplex_tree_ref` |
| | * :doc:`witness_complex_ref` |
+---------------------------------------------+----------------------------------------------------------------------+
|
