Related papers: Transversality and Lipschitz-Fredholm maps
In this paper we prove an infinite-dimensional version of Sard's theorem for Fr\'{e}chet manifolds. Let $ M $ and $ N $ be bounded Fr\'{e}chet manifolds such that the topologies of their model Fr\'{e}chet spaces are defined by metrics with…
Let $F$ be a smooth foliation on a closed Riemannian manifold $M$, and let $\Lambda$ be a transverse invariant measure of $F$. Suppose that $\Lambda$ is absolutely continuous with respect to the Lebesgue measure on smooth transversals. Then…
The main objective of this article is to extend the concept of transversality to supergeometry. Transversality has two important properties in the classical case, namely " stability" and " genericity", which we show in the following that in…
In this note we review some results on the transversality conditions for a smooth Fredholm map $f: X \times (0,T) \to Y$ between two Banach spaces $X,Y$. These conditions are well-known in the realm of bifurcation theory and commonly…
In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the…
We present some transversality results for a category of Fr\'{e}chet manifolds, the so-called $MC^k$-Fr\'{e}chet manifolds. In this context, we apply the obtained transversality results to construct the degree of nonlinear Fredholm mappings…
In this paper, we study Lipschitz-Fredholm vector fields on Bounded-Fr\'{e}chet-Finsler manifolds. In this context we generalize the Morse-Sard-Brown theorem, asserting that if $M$ is a connected smooth bounded-Fr\'{e}chet-Finsler manifold…
We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: the submanifold of configurations of points on an arbitrary submanifold of Euclidean space may be…
We present a definable smooth version of the Thom transversality theorem. We show further that the set of non-transverse definable smooth maps is nowhere dense in the definable smooth topology. Finally, we prove a definable version of a…
Sard's theorem asserts that the set of critical values of a smooth map from one Euclidean space to another one has measure zero. A version of this result for infinite-dimensional Banach manifolds was proven by Smale for maps with Fredholm…
The following theorem is proved: Let M be a locally Lipschitz hypersurface in C^n with one-sided extension property at each point (e.g., without analytic discs). Let S be a closed subset of M and f : M \ S ---> C^m \ E is a CR-mapping of…
We prove a global implicit function theorem. In particular we show that any Lipschitz map $f:\bR^n\times \bR^m\to\bR^n$ (with $n$-dim. image) can be precomposed with a bi-Lipschitz map $\bar{g}:\bR^n\times \bR^m\to \bR^n\times \bR^m$ such…
We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in…
We show that every smooth manifold admits a smooth triangulation transverse to a given smooth map. This removes the properness assumption on the smooth map used in an essential way in Scharlemann's construction [5].
A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the…
The purpose of this short paper is to further develop the theory of transverse generalized complex structures. We focus on proving some equivalent conditions to the basic $dd^{\mathcal{J}}$ -lemma. We justify our approach by describing the…
We study the stability of Triebel-Lizorkin regularity of bounded functions and Lipschitz functions under bi-Lipschitz changes of variables and the regularity of the inverse function of a Triebel-Lizorkin bi-Lipschitz map in Lipschitz…
We consider holomorphic mappings $H$ between a smooth real hypersurface $M\subset \bC^{n+1}$ and another $M'\subset \bC^{N+1}$ with $N\geq n$. We provide conditions guaranteeing that $H$ is transversal to $M'$ along all of $M$. In the…
We prove that all K-homology classes of the stable (and unstable) Ruelle algebra of a Smale space have explicit Fredholm module representatives that are finitely summable on the same smooth subalgebra and with the same degree of…
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…