Related papers: Lipschitz Simplicial Volume of Connected Sums

We present a general framework, treating Lipschitz domains in Riemannian manifolds, that provides conditions guaranteeing the existence of norming sets and generalized local polynomial reproduction - a powerful tool used in the analysis of…

For each strongly connected finite-dimensional (pure) simplicial complex we construct a finite group, the group of projectivities of the complex, which is a combinatorial but not a topological invariant. This group is studied for…

The simplicial volume of oriented closed connected smooth manifolds that admit a non-trivial smooth $S^1$-action vanishes. In the present work we prove a version of this result for the integral foliated simplicial volume of aspherical…

We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on…

Let $X$ be a closed, four-dimensional, oriented, smooth manifold with a Riemannian metric, $g$, let $G$ be a compact Lie group, and $P$ be a principal $G$ bundle over $X$. D. Groisser and T. Parker (1987, 1989) and S. K. Donaldson (1990)…

We show that the integral foliated simplicial volume of a connected compact oriented smooth manifold with a regular foliation by circles vanishes.

Real or complex polynomial mappings between affines spaces admitting a Lipschitz-trivial value are completely characterized.

We prove an additivity property for the normalized Seiberg-Witten invariants with respect to the universal abelian cover of those 3-manifolds, which are obtained via negative rational Dehn surgeries along connected sum of algebraic knots.…

We show that a noncompact manifold with bounded sectional curvature, whose ends are sufficiently Gromov-Hausdorff close to rays, has a finite dimensional space of square-integrable harmonic forms. In the special case of a finite-volume…

Using the monotonicity formulas of Colding and Minicozzi, we prove that on any complete, non-parabolic Riemannian manifold $(M^3, g)$ with non-negative Ricci curvature, the asymptotic weighted scaling invariant integral of scalar curvature…

It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…

We extend two results known for aspherical 3-manifolds to $PD_3$-pairs $(P,\partial{P})$ with aspherical ambient space $P$. Every such $PD_3$-pair may be assembled by attaching 1-handles to $PD_3$-pairs with aspherical; ambient space and…

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt…

We show that the minimal volume entropy of closed manifolds remains unaffected when nonessential manifolds are added in a connected sum. We combine this result with the stable cohomotopy invariant of Bauer-Furuta in order to present an…

We show that a locally Ahlfors 2-regular and locally linearly locally contractible metric surface is locally quasisymmetrically equivalent to the disk. We also discuss an application of this result to the problem of characterizing surfaces…

We prove that in a compact Riemannian manifold, the $m$-minimal clusters of sufficiently small total volume are connected and with small diameter, while in a more general Finsler manifold they are done by at most $m$ connected components of…

We prove a Lipschitz-Volume rigidity theorem in Alexandrov geometry, that is, if a 1-Lipschitz map $f\colon X=\amalg X_\ell\to Y$ between Alexandrov spaces preserves volume, then it is a path isometry and an isometry when restricted to the…

We show how higher-genus su(N) fusion multiplicities may be computed as the discretized volumes of certain polytopes. The method is illustrated by explicit analyses of some su(3) and su(4) fusions, but applies to all higher-point and…

We prove various results on the cohomology of arithmetic lattices arising from quaternion algebras over a number field with at least one complex place, including a strong restriction on the allowable weights of cuspidal cohomological…

We show, in this note, that on any symplectic supermanifold, even or odd, there exist an infinite dimensional affine space of symmetric connections, compatible to the symplectic form.