Related papers: Unimodular invariants of totally real tori in C^n
The $n$-torus is the the unique closed manifold supporting a set of $n$ linearly independent closed $1$-forms. In this paper we improve on this result and show that the torus is the unique closed $n$-dimensional manifold supporting a…
We study a germ of real analytic $n$-dimensional submanifold of ${\mathbf C}^n$ that has a complex tangent space of maximal dimension at a CR singularity. Under the condition that its complexification admits the maximum number of deck…
We extend the Altmann-Hausen presentation of normal affine algebraic C-varieties endowed with effective torus actions to the real setting. In particular, we focus on actions of quasi-split real tori, in which case we obtain a simpler…
An n-dimensional quantum torus is a twisted group algebra of the group $\Z^n$. It is called rational if all invertible commutators are roots of unity. In the present note we describe a normal form for rational n-dimensional quantum tori…
We provide a complete description of normal affine algebraic varieties over the real numbers endowed with an effective action of the real circle, that is, the real form of the complex multiplicative group whose real locus consists of the…
We introduce a new family of invariants of real algebraic sets defined in terms of the topology of their complexifications and compute some of these invariants for spheres. This allows us to completely classify topological isomorphism…
We modify the standard perfect symmetric obstruction theory for moduli spaces of simple perfect complexes, to the situation of complexes on abelian threefolds with fixed determinant and Fourier-Mukai determinant. As outcome we attach…
Ruan-Tian deformations of the Cauchy-Riemann operator enable a geometric definition of (standard) Gromov-Witten invariants of semi-positive symplectic manifolds in arbitrary genera. We describe an analogue of these deformations compatible…
An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus…
We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic threefold. In some cases, our invariants provide lower bounds for…
A general question behind this paper is to explore a good notion for intrinsic curvature in the framework of noncommutative geometry started by Alain Connes in the 80s. It has only recently begun (2014) to be comprehended via the intensive…
Computing topological invariants of 3-manifolds is generally intractable, yet specialized algebraic structures can enable efficient algorithms. For Witten-Reshetikhin-Turaev (WRT) invariants of torus bundles, we exploit the non-commutative…
This paper deals with a new analytic type of vector- and Clifford algebra valued automorphic forms in one and two vector variables. For hypercomplex generalizations of the classical modular group and their arithmetic congruence subgroups…
In this paper we present efficient algorithms for the computation of several invariant objects for Hamiltonian dynamics. More precisely, we consider KAM tori (i.e diffeomorphic copies of the torus such that the motion on them is conjugated…
A general invariant manifold theorem is needed to study the topological classes of smooth dynamical systems. These classes are often invariant under renormalization. The classical invariant manifold theorem cannot be applied, because the…
The real torus manifolds are a generalization of small covers, and the Dold manifolds of real torus type are a class of non-trivial fibre bundles over the projective product spaces with real torus manifolds as fibres. In this paper, first,…
A toric manifold is a compact non-singular toric variety equipped with a natural half-dimensional compact torus action. A torus manifold is an oriented, closed, smooth manifold of dimension $2n$ with an effective action of a compact torus…
Let $T^n$ denote the n-dimensional torus. The class of the bounded operators on $L^2(T^n)$ with analytic orbit under the action of $T^n$ by conjugation with the translation operators is shown to coincide with the class of the zero-order…
We calculate the integral equivariant cohomology, in terms of generators and relations, of locally standard torus orbifolds whose odd degree ordinary cohomology vanishes. We begin by studying GKM-orbifolds, which are more general, before…
We consider symplectic manifolds with Hamiltonian torus actions which are "almost but not quite completely integrable": the dimension of the torus is one less than half the dimension of the manifold. We provide a complete set of invariants…