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1990•Transactions of the American Mathematical SocietyOpen access

Homotopy theory of minimal simplicial spaces

Mark D. Pritt

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Abstract

Various aspects of homotopy theory in the category of minimal simplicial spaces are studied. It is shown that the usual results of homotopy theory hold in this category, and necessary and sufficient conditions are given under which a simplicial space has the homotopy type of a minimal simplicial space. Continuous cohomology in this category is also studied.

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Various aspects of homotopy theory in the category of minimal simplicial spaces are studied. It is shown that the usual results of homotopy theory hold in this category, and necessary and sufficient conditions are given under which a simplicial space has the homotopy type of a minimal simplicial space. Continuous cohomology in this category is also studied.

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Available abstract

Various aspects of homotopy theory in the category of minimal simplicial spaces are studied. It is shown that the usual results of homotopy theory hold in this category, and necessary and sufficient conditions are given under which a simplicial space has the homotopy type of a minimal simplicial space. Continuous cohomology in this category is also studied.

Key concepts: Mathematics, Simplicial set, Homotopy, n-connected, Abstract simplicial complex, h-vector, Homotopy category, Simplicial approximation theorem

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