Related papers: A splitting theorem for good complexifications

For a closed manifold $M$, let Fib$(M)$ be the number of distinct fiberings of $M$ as a fiber bundle with fiber a closed surface. In this paper we give the first computation of Fib$(M)$ where $1<\text{Fib}(M)<\infty$ but $M$ is not a…

In this paper, we prove several rigidity results for complete noncompact manifolds with nonnegative intermediate curvatures. We show that when either $3\leq n\leq 5$, $1\leq m\leq n-1$, or $6\leq n\leq 7$, $m\in \{1,n-1,n-2\}$, any manifold…

We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $n\geq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or the total space of an orbifiber bundle over $\mathbb{S}^1$…

A split of a polytope $P$ is a (regular) subdivision with exactly two maximal cells. It turns out that each weight function on the vertices of $P$ admits a unique decomposition as a linear combination of weight functions corresponding to…

We give a classification of many closed Riemannian manifolds M whose universal cover possesses a nontrivial amount of symmetry. More precisely, we consider closed Riemannian manifolds $M$ such that Isom$(\widetilde{M})$ has noncompact…

This paper gives a uniform, self-contained and direct approach to a variety of obstruction-theoretic problems on manifolds of dimension 7 and 6. We give necessary and sufficient cohomological criteria for the existence of various…

In our previous paper, we studied the category of semifinite bundles on a proper variety defined over a field of characteristic 0. As a result, we obtained the fact that for a smooth projective curve defined over an algebraically closed…

For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct non-large vector subspaces in the rational homology of finitely generated groups. The functorial properties of this…

We study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if…

We give a combinatorial proof of a theorem first proved by Souto which says the following. Let M_1 and M_2 be simple 3-manifolds with connected boundary of genus g>0. If M_1 and M_2 are glued via a complicated map, then every minimal…

In this paper, we explore the theme of orbifold stratified spaces and establish a general criterion for them to be smooth orbifolds. This criterion utilizes the notion of linear stratification on the gluing bundles for the orbifold…

In this paper, we prove fibration theorems for manifolds with almost nonnegative Ricci curvature and certain extra regularity assumptions. We show that a closed $n$-manifold $M$ satisfying $\mathrm{diam}(M)^2\mathrm{sec}_M \geq -\kappa$ and…

Let M be a closed, connected, orientable 3-manifold. The purpose of this paper is to study the Seiberg-Witten Floer homology of M given that S^1 X M admits a symplectic form. In particular, we prove that M fibers over the circle if M has…

Two criteria for a closed connected definite 4-manifold with infinite cyclic fundamental group to be TOP-split are given. One criterion extends a sufficient condition made in a previous paper. The result is equivalent to a purely algebraic…

A consequence of the Cheeger-Gromoll splitting theorem states that for any open manifold $(M,x)$ of nonnegative Ricci curvature, if all the minimal geodesic loops at $x$ that represent elements of $\pi_1(M,x)$ are contained in a bounded…

We give an example of a vector bundle E on a relative curve C --> Spec Z such that the restriction to the generic fiber in characteristic zero is semistable but such that the restriction to positive characteristic p is not strongly…

We investigate the homogeneity of certain kind of slices of the complete complexification of a proper complex equifocal submanifold in a symmetric space of non-compact type.

We show that manifolds admitting special generic maps also admit nice generalized multisections. Special generic maps are natural generalized versions of Morse functions with exactly two singular points on closed manifolds, characterizing…

Let N a compact complex submanifold of a compact complex manifold M. We say N splits in M, if the holomorphic tangent bundle sequence splits holomorphically. By a result of Mok a splitting submanifold of a Kaehler Einstein manifold with a…

We prove that the group of isometries preserving a metric foliation on a closed Alexandrov space $X$ is a closed subgroup of the isometry group of $X$. We obtain a sharp upper bound for the dimension of this subgroup and show that, when…