Bordism and Cobordism Theories
Cobordism studies manifolds, where a manifold is regarded as "trivial" if it is the boundary of another compact manifold. The cobordism classes of manifolds form a ring that is usually the coefficient ring of some generalized cohomology theory. There are many such theories, corresponding roughly to the different structures that one can put on a manifold.
The functors of cobordism theories are often represented by Thom spaces of certain groups.
Read more about this topic: List Of Cohomology Theories
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“The theories and speculations of men concern us more than their puny accomplishment. It is with a certain coldness and languor that we loiter about the actual and so-called practical.”
—Henry David Thoreau (1817–1862)