On the Join of Two Complexes
نویسنده
چکیده
2. Definition of the join (Ki, K2) of Ki and K2. To define the join of two complexes we first define the join (o-, r) of a ^-dimensional simplex a and a g-dimensional simplex r, p, <7 = 0, 1, • • • . This join is a (£+<Z + l)-dimensional simplex with a ^-dimensional side associated with a and the opposite side, which is ^-dimensional, associated with r. These sides will not be distinguished from a and r, respectively. Now consider the complexes K\ and K2. Consider the set consisting of the simplexes <ra of Ki, the simplexes rp of K2, and the simplexes (crat T/S). In a natural way this set forms a complex. We define the join (Ki, K2) of Ki and K2 to be the first barycentric subdivision of this complex.
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