Related papers: Manifolds not containing Gompf nuclei

This is a very short and elementary introduction to G_2 manifolds. We stress the similarities and the differences with K\"ahler manifolds in general and with Calabi-Yau manifolds in particular.

We prove that some aspherical manifolds do not have BIP, negating a question of Jiang.

The existence or non-existence of Einstein metrics on 4-manifolds with non-trivial fundamental group and the relation with the underlying differential structure are analyzed. For most points $(n,m)$ in a large region of the integer lattice,…

Some of the 124 toric Fano 4-folds contain abelian surfaces but most do not: in a few cases it is not known whether they do or not. By elementary methods, with a little computer help, we exclude some more possibilities.

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.

Quiver flag zero loci are subvarieties of quiver flag varieties cut out by sections of homogeneous vector bundles. We prove the Abelian/non-Abelian Correspondence in this context: this allows us to compute genus zero Gromov--Witten…

We prove that 1) There exist infinitely many non-trivial codimension one "thick" knots in $\mathbb{R}^5$; 2) For each closed four-dimensional smooth manifold $M$ and for each sufficiently small positive $\epsilon$ the set of isometry…

Let $N$ be a closed orientable connected $n$-manifold, $n\ge 4$. We classify embeddings of the punctured manifold $N_0$ into $\R^{2n-1}$ up to isotopy. Our result in some sense extends results of J.C. Becker -- H.H. Glover (1971) and O.…

A natural approach to the construction of nearly G2 manifolds lies in resolving nearly G2 spaces with isolated conical singularities by gluing in asymptotically conical G2 manifolds modelled on the same cone. If such a resolution exits, one…

For each integer $n$ we construct a simply connected $4$-manifold $X$ admitting a smoothly embedded surface $\Sigma$ of self intersection number $n$ such that the complement of the surface has non-trivial fundamental group. This answers a…

We prove Gagliardo-Nirenberg inequalities on some classes of manifolds, Lie groups and graphs.

$G_2$-monopoles are solutions to gauge theoretical equations on $G_2$-manifolds. If the $G_2$-manifolds under consideration are compact, then any irreducible $G_2$-monopole must have singularities. It is then important to understand which…

We are concerned with the existence and asymptotic behavior of multiple radial sign-changing solutions with the nodal characterization for a Kirchhoff-type problem involving the nonlinearity $|u|^{p-2}u(2<p<4)$ in $\mathbb{R}^3$. By…

We show that the Riemannian Kerr solutions are the only Riemannian, Ricci-flat and asymptotically flat ${\rm C}^{2}$-metrics $g_{\mu\nu}$ on a 4-dimensional complete manifold ${\cal M}$ of topology ${\rm R}^{2} \times {\rm S}^{2}$ which…

Here we show that every compact smooth 4-manifold X has a structure of a Broken Lefschetz Fibration (BLF in short). Furthermore, if b_{2}^{+}(X)> 0 then it also has a Broken Lefschetz Pencil structure (BLP) with nonempty base locus. This…

We establish a gluing theorem for monopoles over 4--manifolds containing long necks. The theorem is stated in terms of an ungluing map defined explicitly in terms of data that appear naturally in applications. Orientations of moduli spaces…

We prove the nonexistence of stable immersed minimal surfaces uniformly conformally equivalent to the complex plane in any complete orientable four-dimensional Riemannian manifold with uniformly positive isotropic curvature. We also…

We introduce the concept of Spin^G-structure in a SO-bundle, where $G\subset U(V)$ is a compact Lie group containing $-id_V$. We study and classify $Spin^G(4)$-structures on 4-manifolds, we introduce the G-Monopole equations associated with…

We prove that all currently known examples of manifolds with nonnegative sectional curvature satisfy a stronger condition: their curvature operator can be modified with a 4-form to become positive-semidefinite.

We construct examples of (effective) closed orbifolds which are covered by manifolds, but not finitely so.