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Jun, 2019
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Cobordisms and Relatted Topics

The complex cobordism MU is one of the most fundamental tools in modern stable homotopy theory . There are many other cobordism groups corresponding to geometric structures on manifolds and they give rise to generalized homology theories .

Even in algebraic geometry , an analogous concept called algebraic cobordism has been introduced. Nowadyas cobordisms are important in the definition of topological quantum field theories .

One of the most famous books on cobordism is Stong’s [ Sto68 ] . For stable homotopy theory, Araki’s book (in Japanese) and Rudyak’s book [ Rud98 ] are useful. It might be interesting to take a look at the book [ NT07 ] of (English translations of) collected papers on cobordism theory compiled by Novikov.

References