About: Path space fibration

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In algebraic topology, the path space fibration over a based space is a fibration of the form where * is the path space of X; i.e., equipped with the compact-open topology. * is the fiber of over the base point of X; thus it is the loop space of X. The space consists of all maps from I to X that may not preserve the base points; it is called the free path space of X and the fibration given by, say, , is called the free path space fibration.

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  • In algebraic topology, the path space fibration over a based space is a fibration of the form where * is the path space of X; i.e., equipped with the compact-open topology. * is the fiber of over the base point of X; thus it is the loop space of X. The space consists of all maps from I to X that may not preserve the base points; it is called the free path space of X and the fibration given by, say, , is called the free path space fibration. The path space fibration can be understood to be dual to the mapping cone. The reduced fibration is called the mapping fiber or, equivalently, the homotopy fiber. (en)
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  • In algebraic topology, the path space fibration over a based space is a fibration of the form where * is the path space of X; i.e., equipped with the compact-open topology. * is the fiber of over the base point of X; thus it is the loop space of X. The space consists of all maps from I to X that may not preserve the base points; it is called the free path space of X and the fibration given by, say, , is called the free path space fibration. (en)
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  • Path space fibration (en)
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