

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.
[NT07]
S. P. Novikov and I. A. Taimanov,
editors.
Topological library.
Part 1: cobordisms and their applications
, volume 39 of
Series on
Knots and Everything
. World Scientific Publishing Co. Pte. Ltd.,
Hackensack, NJ, 2007. Translation by V. O. Manturov.
[Rud98]
Yuli B. Rudyak.
On Thom spectra, orientability, and cobordism
. Springer Monographs in Mathematics.
SpringerVerlag, Berlin, 1998.
[Sto68]
Robert E. Stong.
Notes on cobordism theory
. Mathematical notes. Princeton University Press,
Princeton, N.J., 1968.


