Related papers: First-order invariants of differential 2-forms

For a Dedekind domain $\mathcal{O}$ and a rank two co-torsion module $M\subseteq \mathcal{O}^2$ with invariant factor ideals $\mathcal{L}\supseteq \mathcal{K}$ in $\mathcal{O}$, that is, $\frac{\mathcal{O}^2}{M}\cong…

We prove that a type II$_1$ factor $M$ can have at most one Cartan subalgebra $A$ satisfying a combination of rigidity and compact approximation properties. We use this result to show that within the class $\Cal H \Cal T$ of factors $M$…

We establish effective versions of Oppenheim's conjecture for generic inhomogeneous quadratic forms. We prove such results for fixed shift vectors and generic quadratic forms. When the shift is rational we prove a counting result which…

Let $M$ and $N$ be smooth manifolds, with $M$ closed and connected. If the $C^r$--diffeomorphism group of $M$ is elementarily equivalent to the $C^s$--diffeomorphism group of $N$ for some $r,s\in[1,\infty)\cup\{0,\infty\}$, then $r=s$ and…

We define the associated variety $ X_{M} $ of a module $ M $ over a finite-dimensional superalgebra $ {\mathfrak g} $, and show how to extract information about $ M $ from these geometric data. $ X_{M} $ is a subvariety of the cone $ X $ of…

We prove that the monodromy diffeomorphism of a complex 2-dimensional isolated hypersurface singularity of weighted-homogeneous type has infinite order in the smooth mapping class group of the Milnor fiber, provided the singularity is not a…

We prove that if $f:I\subset \Bbb R\to \Bbb R$ is of bounded variation, then the noncentered maximal function $Mf$ is absolutely continuous, and its derivative satisfies the sharp inequality $\|DMf\|_1\le |Df|(I)$. This allows us obtain,…

We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S_3, the dihedral group D_4 and the quaternion group Q. Poincare' duality holds in every case, and under some…

In this paper we consider a diffeomorphism $f$ of a compact manifold $M$ which contracts an invariant foliation $W$ with smooth leaves. If the differential of $f$ on $TW$ has narrow band spectrum, there exist coordinates $H _x:W_x\to T_xW$…

Let ${\cal F}_\lambda$ be the space of tensor densities on ${\bf R}^n$ of degree $\lambda$ (or, equivalently, of conformal densities of degree $-\lambda{}n$) considered as a module over the Lie algebra $so(p+1,q+1)$. We classify…

We suggest an effective procedure to calculate numerical invariants for rank two bundles over blown-up surfaces. We study the moduli spaces M_j of bundles on the blown-up plane splitting over the exceptional divisor as O(j)+O(-j). We use…

We compute invariants for the two-variable M\"obius transformation. In particular we are interested in partial differential equations in two dependent and two independent variables that are kept invariant under this transformation.

We consider a class of smooth mixing flows $T^{\alpha,\gamma}$ on $\mathbb{T}^2$ with one degenerated fixed point $x_0\in \mathbb{T}^2$ of power type $\gamma\in (-1,0)$. We prove that for a $G_\delta$ dense set of $\alpha\in \mathbb{T}$, a…

We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\cn{n}$ fixing the orbits of a regular vector field. We reduce the formal classification problem to solve a…

A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative.

We determine the number of functionally independent components of tensors involving higher-order derivatives of a Riemannian metric.

For a finite group $G$ acting faithfully on a finite dimensional $F$-vector space $V$, we show that in the modular case, the top degree of the vector coinvariants grows unboundedly: $\lim_{m\to\infty} \topdeg F[V^{m}]_{G}=\infty$. In…

In the context of the Higher-Order Maxwell-Einstein-Scalar (HOMES) theories, which are invariant under spacetime diffeomorphisms and $U(1)$ gauge symmetry, we study two broad subclasses: the first is up to linear in $R_{\mu\nu\alpha\beta}$,…

Let $\Omega$ be an open set in Euclidean space with finite Lebesgue measure $|\Omega|$. We obtain some properties of the set function $F:\Omega\mapsto \R^+$ defined by $$ F(\Omega)=\frac{T(\Omega)\lambda_1(\Omega)}{|\Omega|} ,$$ where…

Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several…