In mathematics, a pseudomanifold is a special type of topological space. It looks like a manifold at most of its points, but it may contain singularities. For example, the cone of solutions of forms a pseudomanifold.
Figure 1: A pinched torus
A pseudomanifold can be regarded as a combinatorial realisation of the general idea of a manifold with singularities. The concepts of orientability, orientation and degree of a mapping make sense for pseudomanifolds and moreover, within the combinatorial approach, pseudomanifolds form the natural domain of definition for these concepts.[1][2]
- ^ Seifert, H.; Threlfall, W. (1980), Textbook of Topology, Academic Press Inc., ISBN 0-12-634850-2
- ^ Spanier, H. (1966), Algebraic Topology, McGraw-Hill Education, ISBN 0-07-059883-5