Einstein's equations stem from General Relativity. In the context of Riemannian manifolds,
an independent mathematical theory has developed around them. Recently, it has produced …

With the introduction of general relativity, it became necessary to express the differential
operators of mathematical physics in a coordinatefree form. This made it possible to define …

This book is based on a one-semester course taught since 2002 at Instituto Superior
Técnico (Lisbon) to mathematics, physics and engineering students. Its aim is to provide a …

This paper studies the rational homotopy groups of the group $\mathrm {Diff}(S^ 4) $ of self-
diffeomorphisms of $ S^ 4$ with the $ C^\infty $-topology. We present a method to prove that …

A new proof is given of the unpublished results of Morlet on the relation between the
homeomorphism group and the diffeomorphism group of a smooth manifold. In particular …

The fundamental groups of complements to algebraic curves in CIp'2 were studied by 0.
Zariski almost 60 years ago (cf.[Z]). He showed that these groups are affected by the type …

Let i: V-pn be a closed embedding of a smooth complex v algebraic variety into the
projective space, VC the dual variety of i (V). Its points parametrize hyperplanes which are …

Major Developments The first big breakthrough, by Kirby and Siebenmann [1969, 1969a,
1977], was an obstruction theory for the problem of triangulating a given topological …

Abstract Let $\mathcal {M} $ denote the space of probability measures on $\mathbb {R}^ D $
endowed with the Wasserstein metric. A differential calculus for a certain class of absolutely …

Given a closed smooth manifold M of even dimension 2 n≥ 6 with finite fundamental group,
we show that the classifying space B Diff (M) of the diffeomorphism group of M is of finite …