In this paper, we establish global boundedness results for the jet determination order of CR maps between (not necessarily bounded) generic submanifolds in complex space. A key feature of our results is that they apply to Nash submanifolds, but do not extend to arbitrary real-analytic submanifolds.
We classify all contact structures on 3-manifolds that admit a nonfree toric action, up to contactomorphism, and present them through explicit topological descriptions. Our classification is based on Lerman's classification of toric contact 3-manifolds up to equivariant contactomorphism [Lerman, J. Symplectic Geom. 1 (2003), 785–828]. We also prove that every contact 3-manifold with a nonfree toric action arises as the concave boundary of a toric linear plumbing over spheres inspired by Marinković et al. As a corollary of both results, we classify which contact 3-manifolds arise as the concave boundary of a linear plumbing of spheres.
We give two short proofs of the abelian Livšic theorem of Gogolev and Rodriguez Hertz. We show that these proofs may be extended to give new abelian Livšic theorems for positive density sets of null-homologous orbits and for amenable covers.
In this paper, we investigate a special autonomous Schwarzian differential equation
We show that the ‘profinite direct sum’ is a good notion of infinite direct sums for profinite modules, having properties similar to those of direct sums of abstract modules. For example, the profinite direct sum of projective modules is projective, and there is a Mackey's formula for profinite modules described using these sums. As an application, we prove that the class of profinite groups of type is closed under subgroups.
We prove that arbitrary simplicial manifolds satisfy Kan conditions in a suitable local sense. This allows us to expand a technique for differentiating higher Lie groupoids worked out in [8] to the setting of general simplicial manifolds. Consequently, we derive a method to differentiate simplicial manifolds into higher Lie algebroids.
To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to -multicomplexes. We present a family of model category structures on the category of -multicomplexes where the weak equivalences are the morphisms inducing a quasi-isomorphism at a fixed page of the first spectral sequence and at a fixed page of the second spectral sequence. Such weak equivalences arise naturally in complex geometry. In particular, the model structures presented here establish a basis for studying homotopy types of almost complex manifolds.
Let and . I construct a -Frostman Borel measure on such that for every . This answers a question of Peres and Schlag.
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