Related papers: $G$-equivariant embedding theorems for CR manifold…

We extend the notion of a fundamental negatively $\mathbb Z$-graded Lie algebra $\mathfrak{m}_x=\bigoplus_{p\leq -1}\mathfrak{m}_x^p$ associated to any point of a Levi nondegenerate CR manifold to the class of $k$-nondegenerate CR manifolds…

In this paper, we consider a closed Riemannian manifold $M^{n+1}$ with dimension $3\leq n+1\leq 7$, and a compact Lie group $G$ acting as isometries on $M$ with cohomogeneity at least $3$. After adapting the Almgren-Pitts min-max theory to…

Given a metric measure space $(X,d,\mathfrak{m})$ that satisfies the Riemannian Curvature Dimension condition, $RCD^*(K,N),$ and a compact subgroup of isometries $G \leq Iso(X)$ we prove that there exists a $G-$invariant measure,…

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new…

Suppose G is a compact Lie group and N is a closed normal subgroup of G acting freely on a smooth manifold X. The Cartan theorem alluded to in the title postulates the existence of a natural isomorphism between the G-equivariant cohomology…

Denote by $\Delta_M$ the $M$-dimensional simplex. A map $f\colon \Delta_M\to\mathbb R^d$ is an almost $r$-embedding if $f\sigma_1\cap\ldots\cap f\sigma_r=\emptyset$ whenever $\sigma_1,\ldots,\sigma_r$ are pairwise disjoint faces. A…

Let $G$ be a compact Lie group. We prove that if $V$ and $W$ are orthogonal $G$-representations such that $V^G=W^G=\{0\}$, then a $G$-equivariant map $S(V) \to S(W)$ exists provided that $\dim V^H \leq \dim W^H$ for any closed subgroup…

We introduce a class of combinatorial hypersurfaces in the complex projective space. They are submanifolds of codimension~2 in $\C P^n$ and are topologically "glued" out of algebraic hypersurfaces in $(\C^*)^n$. Our construction can be…

Schoen-Webster theorem asserts a pseudoconvex CR manifold whose automorphism group acts non properly is either the standard sphere or the Heisenberg space. The purpose of this paper is to survey successive works around this result and then…

We prove an analog of the classical Hartogs extension theorem for CR $L^{2}$ functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a problem posed…

Let M be a smooth CR manifold of CR dimension n and CR codimension k, which is not compact, but has the local extension property E. We introduce the notion of "elementary pseudoconcavity" for M, which extends to CR manifolds the concept of…

We prove that if $G$ is a noncompact connected real reductive linear Lie group, then any discrete subgroup of $G$ acting properly discontinuously and cocompactly on some homogeneous space $G/H$ of $G$ is quasi-isometrically embedded and…

We prove a version of Whitney's strong embedding theorem for isometric embeddings within the general setting of the Nash-Kuiper h-principle. More precisely, we show that any $n$-dimensional smooth compact manifold admits infinitely many…

We show that the theory of stable complex $G$-cobordisms, for a torus $G$, is embedded into the theory of stable complex $G$-cobordisms of not necessarily compact manifolds equipped with proper abstract moment maps. Thus the introduction of…

In this paper, we develope an equivariant theory of Chern characters for coherent sheaves on compact complex manifolds with finite group actions, taking values in Bott-Chern cohomology classes. Furthermore, we establish the corresponding…

It was shown by Samelson and Wang that each compact Lie group K of even dimension admits left-invariant complex structures. When K has odd dimension it admits a left-invariant CR-structure of maximal dimension. This has been proved recently…

A continuous map C^d -> C^N is a complex k-regular embedding if any k pairwise distinct points in C^d are mapped by f into k complex linearly independent vectors in C^N. Our central result on complex k-regular embeddings extends results of…

It is proved that if $G$ is a compact Lie group, then an equivariant Serre fibration of $G$-CW-complexes is an equivariant Hurewicz fibration in the class of compactly generated $G$-spaces. In the nonequivariant setting, this result is due…

Consider a finite-dimensional real vector space equipped with a finite group acting unitarily on it. We address the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our approach is based on…

We construct examples of nondegenerate CR manifolds with Levi form of signature $(p,q)$, $2\leq p\leq q$, which are compact, not locally CR flat, and admit essential CR vector fields. We also construct an example of a noncompact…