This article addresses the problem of unsupervised learning of multiple linear manifolds in a topology preserving neural map. The model finds simple linear estimations of the regions of the unknown data manifold. Each neuron of the map corresponds to a linear manifold whose basis and mean vectors and on- and off-manifold standard deviations must be learnt. The learning rules are derived based on competition between neurons and maximizing an approximation of the mutual information between the input and the output of each neuron. Neighborhood functions are also considered in the learning rules in order to develop the topology preserving property for the map. Considering two special density models for the input data, the optimal nonlinear input/output mappings of the neurons are found. Experimental results show a good performance for the proposed method on synthesized and practical problems compared with other relevant techniques.