Related papers: Smooth Extensions and Spaces of Smooth and Holomor…

The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit totally geodesic, holomorphic complex homothetic foliation by curves.

We classify up to diffeomorphism all smooth manifolds homeomorphic to the complex projective m-space $\mathbb{C}P^{m}$ for $m = 5, 6, 7$ and $8$. As an application, for $m = 7$ and $8$, we compute the smooth tangential structure set of…

A compact K\"ahler manifold is shown to be simply-connected if its `symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective…

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the…

For a smoothing Y of a 2-dimensional cyclic quotient singularity X, we construct a simple handle decomposition of Y by using a particular birational map from Y to the projective plane. The manifold Y is built up from the product of an…

Let $\Phi$ be a flow on a smooth, compact, finite-dimensional manifold $M$. Consider the subsets $E(\Phi)$ and $D(\Phi)$ of $C^{\infty}(M,M)$ consisting of smoothh mappings and diffeomorphisms (respectively) of $M$ preserving the foliation…

We show that for topological groups and loop contractible coefficients the cohomology groups of continuous group cochains and of group cochains that are continuous on some identity neighbourhood are isomorphic. Moreover, we show a similar…

We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves even globally, but under an assumption.

A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…

We give necessary and sufficient conditions for both square integrability and smoothness for densities of a probability measure on a compact connected Lie group.

The simplest case of a manifold with singularities is a manifold M with boundary, together with an identification of the boundary with a product M1 x P, where P is a fixed manifold. The associated singular space is obtained by collapsing P…

We consider compact symplectic manifolds acted on effectively by a compact connected Lie group $K$ in a Hamiltonian fashion. We prove that the squared moment map $||\mu||^2$ is constant if and only if $K$ is semisimple and the manifold is…

This paper proposes a new notion of smoothness of algebras, termed differential smoothness, that combines the existence of a top form in a differential calculus over an algebra together with a strong version of the Poincar\'e duality…

It is well-known that an effective orbifold M (one for which the local stabilizer groups act effectively) can be presented as a quotient of a smooth manifold P by a locally free action of a compact lie group K. We use the language of…

In this paper, we investigate the topology of a class of non-K\"ahler compact complex manifolds generalizing that of Hopf and Calabi-Eckmann manifolds. These manifolds are diffeomorphic to special systems of real quadrics in $\Bbb C^n$…

We generalize Cartan's logarithmic derivative of a smooth map from a manifold into a Lie group $G$ to smooth maps into a homogeneous space $M=G/H$, and determine the global monodromy obstruction to reconstructing such maps from…

In this paper, we construct round fold maps or stable fold maps with concentric singular value sets introduced by the author on smooth bundles over spheres or bundles over more general manifolds. The class of round fold maps includes…

The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately…

We consider conformal actions of simple Lie groups on compact Lorentzian manifolds. Mainly motivated by the Lorentzian version of a conjecture of Lichnerowicz, we establish the alternative: Either the group acts isometrically for some…

We prove an analogue of E. Levi's Continuity Principle for meromorphic mappings with values in arbitrary compact complex manifolds in place of the Riemann sphere $\cc\pp^1$. The result is achieved by introducing a new extension method for…