Geodesic
Homology of Deleted Products of Contractible 2-Dimensional Polyhedra. III
Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1217-1223

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Our aim in this paper is to continue our investigation of the homology of deleted products of finite, contractible, 2-dimensional polyhedra. In [1], we observed that if X is such a polyhedron, then a homeomorph of X can be constructed by starting with a 2-simplex and appending n-simplexes (n = 1, 2). In this paper, we are concerned with those polyhedra which have the property that if they are constructed as above, then at some stage we are forced to add to X i–1 a 2-simplex τ at two of its 1-faces, 〈u 3, u 1〉 and 〈u 3, u 2〉, where there is a simple closed curve S in ∂(St(u 3, X i–1)) such that u 1 and u 2 are not in S but every sequence of 1-simplexes in ∂(St(u 3, X i–1)) from u 1 to u 2 intersects S. The cone over the complete graph on five vertices and the cone over the houses-and-wells figure are examples of such spaces. 
Patty, C. W. Homology of Deleted Products of Contractible 2-Dimensional Polyhedra. III. Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1217-1223. doi: 10.4153/CJM-1970-140-5
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[1] 1. Patty, C. W., Homology of deleted products of contractible 2-dimensional polyhedra. I, Can. J. Math. 20 (1968), 416–441. Google Scholar

[2] 2. Patty, C. W., Homology of deleted products of contractible 2-dimensional polyhedra. II, Can. J. Math. 20 (1968), 842–854. Google Scholar

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