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+/*    This file is part of the Gudhi Library. The Gudhi library
+ *    (Geometric Understanding in Higher Dimensions) is a generic C++
+ *    library for computational topology.
+ *
+ *    Author:       François Godi, Vincent Rouvreau
+ *
+ *    Copyright (C) 2017  INRIA
+ *
+ *    This program is free software: you can redistribute it and/or modify
+ *    it under the terms of the GNU General Public License as published by
+ *    the Free Software Foundation, either version 3 of the License, or
+ *    (at your option) any later version.
+ *
+ *    This program is distributed in the hope that it will be useful,
+ *    but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *    GNU General Public License for more details.
+ *
+ *    You should have received a copy of the GNU General Public License
+ *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#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    Fran&ccedil;ois 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_