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 کاملInverting the Motivic Bott Element
We prove a version for motivic cohomology of Thomason’s theorem on Bott-periodic K-theory, namely, that for a field k containing the nth roots of unity, the mod n motivic cohomology of a smooth k-scheme agrees with mod n étale cohomology, after inverting the element in H(k, Z/n(1)) corresponding to a primitive nth root of unity.
متن کاملBelief Affirming in Learning Processes*
A learning process is belief affirming if the difference between a player's expected payoff in the next period, and the average of his or her past payoffs converges to zero. We show that every smooth discrete fictitious play and every continuous fictitious play is belief affirming. We also provide conditions under which general averaging processes are belief affirming. Journal of Economic Liter...
متن کاملRemembering Raoul Bott
Figure 1. Raoul Bott in 2002. Raoul Bott passed away on December 20, 2005. Over a five-decade career he made many profound and fundamental contributions to geometry and topology. This is the second part of a two-part article in the Notices to commemorate his life and work. The first part was an authorized biography, “The life and works of Raoul Bott” [4], which he read and approved a few years ...
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: Physics
سال: 2020
ISSN: 1943-2879
DOI: 10.1103/physics.13.s147