Related papers: Manifolds with analytic corners

Let $M$ be a compact connected surface with boundary. We prove that the signal condition given by the Gauss-Bonnet theorem is necessary and sufficient for a given smooth function $f$ on $\partial M$ (resp. on $M$) to be geodesic curvature…

A Seifert manifold is a 3-dimensional manifold with a circle action. It is a circle bundle (with singularities) over a 2-dimensional orbifold. In this note, we discuss a generalized Seifert manifolds. By definition, they have bundle-like…

We introduce the metric fundamental class for metric spaces that are homeomorphic to compact, non-orientable, smooth manifolds with (possibly empty) boundary. This is an integer rectifiable current that provides an analytic representation…

Previous work has shown that reverse differential categories give an abstract setting for gradient-based learning of functions between Euclidean spaces. However, reverse differential categories are not suited to handle gradient-based…

In this paper, an explicit classification result for certain 5-manifolds with fundamental group Z/2 is obtained. These manifolds include total spaces of circle bundles over simply-connected 4-manifolds.

A smooth stably complex manifold is called a totally tangentially/normally split manifold (TTS/TNS-manifold, for short, resp.) if the respective complex tangential/normal vector bundle is stably isomorphic to a Whitney sum of complex linear…

We study relations among characteristic classes of smooth manifold bundles with highly-connected fibers. For bundles with fiber the connected sum of $g$ copies of a product of spheres $S^d \times S^d$ and an odd $d$, we find numerous…

One says that a smooth manifold M is a pseudo-Riemannian manifold of signature (p,q) if the tangent bundle TM is equipped with a smooth non-degenerate symmetric inner product g of signature (p,q). Similarly one says that M is an affine…

This paper explores a new perspective on the universality of the vertical lift in tangent categories by presenting a categorification of the dimension of smooth manifolds. The universality of the vertical lift is a key part of the axioms of…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

We prove vanishing results for the generalized Miller-Morita-Mumford classes of some smooth bundles whose fiber is a closed manifold that supports a nonpositively curved Riemannian metric. We also find, under some extra conditions, that the…

This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds arise from varying hypotheses on the surface…

In the first part of this note, we discuss the compact K\"ahler manifold with a strongly pseudo-effective tangent bundle. In the second part, we give new proof of the fact that the only projective manifolds with the big tangent bundle are…

If $X$ is a smooth manifold then the $\mathbb R$-algebra $C^\infty(X)$ of smooth functions $c:X\to\mathbb R$ is a $C^\infty$-$ring$. That is, for each smooth function $f:{\mathbb R}^n\to\mathbb R$ there is an $n$-fold operation…

We study the geometric properties of the base manifold for the unit tangent bundle satisfying the $\eta$-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of…

We generalise the classical Chern-Gauss-Bonnet formula to a class of 4-dimensional manifolds with finitely many conformally flat ends and singular points. This extends results of Chang-Qing-Yang in the smooth case. Under the assumptions of…

We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting between sections of complex vector bundles E,F over a compact smooth manifold M with smooth boundary N. We describe the analytic…

We give a new criterion for when a resolution of a surface of general type with canonical singularities has big cotangent bundle and a new lower bound for the values of $d$ for which there is a surface with big cotangent bundle that is…

In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological…

We define an analytic index and prove a topological index theorem for a non-compact manifold $M\_0$ with poly-cylindrical ends. We prove that an elliptic operator $P$ on $M\_0$ has an invertible perturbation $P+R$ by a lower order operator…