Abstract. A real Bott manifold is the total space of iterated RP 1 bundles starting with a point, where each RP 1 bundle is projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their cohomology rings with Z/2 coefficients are isomorphic. A real Bott manifold is a real toric manifold and admits a flat riemannian metric invariant u...

The weak-strong uniqueness for Maxwell--Stefan systems and some generalized is proved. corresponding parabolic cross-diffusion equations are considered in a bounded domain with no-flux boundary conditions. key points of the proofs various inequalities relative entropy associated analysis spectrum quadratic form capturing frictional dissipation. latter task complicated by singular nature diffusi...

This paper is devoted to classical Bott periodicity, its history and more recent extensions in algebraic and Hermitian K-theory. However, it does not aim at completeness. For instance, the variants of Bott periodicity related to bivariant K-theory are described by Cuntz in this handbook. As another example, we don’t emphasize here the relation between motivic homotopy theory and Bott periodicit...

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 ...

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(...