For a real vector bundle over a compact base, its Thom space is the quotient of its disk bundle by its sphere bundle, with the collapsed sphere bundle as basepoint. Equivalently it is the one-point compactification of the total space. An oriented bundle's Thom class and Thom isomorphism identify the reduced cohomology of this space with shifted cohomology of the base.
In topology, a Thom space is a certain type of construction associated with smooth manifolds and more generally, with smooth approximations to certain spaces. Named after the mathematician René Thom, Thom spaces arise in the context of studying the topology of manifold bundles and intersection theory.
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