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1970•Transactions of the American Mathematical SocietyOpen access

Homology of deleted products of one-dimensional spaces

Arthur H. Copeland, C. W. Patty

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Abstract

The object of this paper is to investigate the homology of deleted products of finitely triangulated one-dimensional spaces. By direct calculation, we obtain upper bounds for the two-dimensional Betti numbers, and, using a rather small system of topological types of spaces appearing as subspaces of the space under consideration, we obtain lower bounds for these Betti numbers. We demonstrate that, in general, the two-dimensional Betti numbers are larger than they were originally thought to be.

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What this paper is about

The object of this paper is to investigate the homology of deleted products of finitely triangulated one-dimensional spaces. By direct calculation, we obtain upper bounds for the two-dimensional Betti numbers, and, using a rather small system of topological types of spaces appearing as subspaces of the space under consideration, we obtain lower bounds for these Betti numbers. We demonstrate that, in general, the two-dimensional Betti numbers are larger than they were originally thought to be.

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Available abstract

The object of this paper is to investigate the homology of deleted products of finitely triangulated one-dimensional spaces. By direct calculation, we obtain upper bounds for the two-dimensional Betti numbers, and, using a rather small system of topological types of spaces appearing as subspaces of the space under consideration, we obtain lower bounds for these Betti numbers. We demonstrate that, in general, the two-dimensional Betti numbers are larger than they were originally thought to be.

Key concepts: Betti number, Mathematics, Linear subspace, Homology (biology), Topological space, Pure mathematics, Discrete mathematics, Combinatorics

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