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The Cohomology Algebra of Polyhedral Product Objects (1804.07907v1)

Published 21 Apr 2018 in math.AT

Abstract: In this paper, we compute the homology group and cohomology algebra of various polyhedral product objects uniformly from the point of view of diagonal tensor product. As applications, we introduce the polyhedral product method into commutative algebra and show that the homotopy types of polyhedral product spaces depend on not only the homotopy type of each summand pair but also on the character coproduct of the pair.

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