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+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author:       François Godi, Vincent Rouvreau
+ *
+ *    Copyright (C) 2017  INRIA
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef DOC_TOPLEX_MAP_INTRO_TOPLEX_MAP_H_
+#define DOC_TOPLEX_MAP_INTRO_TOPLEX_MAP_H_
+
+// needs namespace for Doxygen to link on classes
+namespace Gudhi {
+
+/**  \defgroup toplex_map Toplex Map
+ * 
+ * \author    François Godi
+ * @{
+ * 
+ * \section toplexmapdefinition Definition
+ *
+ * A Toplex_map is a data structure to represent and store a simplicial complex. A "toplex" is the contraction of
+ * "top-simplex", also known as a maximal simplex. The plural form of "toplex" will be called "toplices".
+ *
+ * Let's consider a simplicial complex, denote by \f$d\f$ its dimension and by \f$k\f$ its number of maximal simplices.
+ * Furthermore, denote by \f$\Gamma_0\f$ the maximal number of toplices, i.e. maximal simplices, that contain a same
+ * vertex.
+ *
+ * The goal of the Toplex Map is both to represent the complex in optimal O(kd) space and to provide fast standard
+ * operations such as : insertion, removal, contraction of an edge, collapses and membership of a simplex. The time
+ * needed for these operation is linear or quadratic in \f$\Gamma_0\f$ and \f$d\f$.
+ *
+ * Toplex map is composed firstly of a raw storage of toplices and secondly of a map which associate any vertex to a
+ * set of pointers toward all toplices containing this vertex. The data structure is described in
+ * \cite boissonnat_et_al:LIPIcs:2015:5098 (aka. Simplex Array List or SAL).
+ *
+ * \image html map.png
+ *
+ * The performances are a lot better than the `Simplex_tree` as soon you use maximal simplices and not simplices
+ * (cf. \cite DBLP:journals/corr/BoissonnatS16 ).
+ *
+ */
+/** @} */  // end defgroup toplex_map
+
+}  // namespace Gudhi
+
+#endif  // DOC_TOPLEX_MAP_INTRO_TOPLEX_MAP_H_