Abstract
This chapter discusses the homotopy type of manifolds. The chapter focuses on certain theorems that refer to a class of manifolds called class II. By an n-dimensional manifold, Mn, is meant a class of combinatorially equivalent, simplicial complexes covering the same space, each complex being a formal manifold, meaning that the complement of each vertex is combinatorially equivalent to An or to An-1, according as the vertex in question is inside Mn or on An, where Ak stands for a closed k-simplex and Mn is the boundary of Mn. The proper triangulations of an unbounded manifold of class C1, or smooth manifold, are C1-triangulations.
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