Bott type periodicity for the higher octonions
نویسندگان
چکیده
منابع مشابه
The Bott Periodicity Theorem
The Bott periodicity theorem is of fundamental importance in many areas of mathematics, from algebraic topology to functional analysis. It appears unexpectedly in different guises and I would like to explain some of these as well as the influence it has had on the development of different fields. I will concentrate on two roles that periodicity plays. First, periodicity allows one to deloop cla...
متن کاملBott periodicity
1 Description The Periodicity Theorem was proved by Raoul Bott over fifty years ago (cf. survey [3], [4], [9]) and quickly became one of the strongest tools in homotopy theory, topology of manifolds and global analysis. The original theorem asserted that homotopy groups of the linear groups GL(n,F) where F is the field of real, complex or quaternion numbers are periodic i.e. πi(GL(k,F) ' πi+nF(...
متن کاملBott Periodicity for Fibred Cusp Operators
In the framework of fibred cusp operators on a manifold X associated to a boundary fibration Φ : ∂X → Y , the homotopy groups of the space G−∞ Φ (X;E) of invertible smoothing perturbations of the identity are computed in terms of the K-theory of T ∗Y . It is shown that there is a periodicity, namely the odd and the even homotopy groups are isomorphic among themselves. To obtain this result, one...
متن کاملA Noncommutative Proof of Bott Periodicity
Bott periodicity in K-theory is a rather mysterious object. The classical proofs typically consist of showing that the unitary groups form an Ω-spectrum from which to get a cohomology theory; then showing that that theory is K-theory; and most formidably showing that U(n) is homotopic to U(n+ 2) for all n. However, Cuntz showed that Bott periodicity can be derived in a much simpler way if one r...
متن کاملBott Periodicity and the Parallelizability of the Spheres
Inti-eduction. The theorems of Bott (4), (5) on the stable homotopy of the classical groups imply that the sphere S is not parallelizable for n 4= 1,3,7. This was shown independently by Kervaire(8) and Milnor(7), (9). Another proof can be found in (3), § 26-11. The work of J. F. Adams (on the non-existence of elements of Hopf invariant one) implies more strongly that S with any (perhaps extraor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2015
ISSN: 1661-6952
DOI: 10.4171/jncg/221