Thom space
= Thom space
{c}
{title2=$\operatorname{Th}(\xi)=D(\xi)/S(\xi)$}
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.