

Ktheory

K
theory appears in various fields in many different
forms. Connections with physics, e.g.
D
brane
in
string theory
and
Verlinde algebra
, have been discovered recently.
See, for example, Atiyah’s “
K
theory Past and Present”
[
Ati
]
. Another very concise introductory text is
Karoubi’s
[
Kar
]
, which seems to be a lecture note of talks at the
Clay Mathematics Institute. There is a lecture note by
Corti驕s
[
Cor
]
on relations among algebraic
K
theory, operator algebraic
K
theory, and topological
K
theory.
One of the reasons of this ubiquitiy of
K
theory might be that taking the Grothendieck group is
a decategorification, an operation inverse to
categorifications
,
One of the most important properties of topological
K
theory is the Bott periodicity. Higher order
periodicities are one of the central themes in
stable homotopy theory
.


