Related papers: $\mathbb{S}ol^3\times\mathbb{E}^1$-manifolds

In this paper we construct various moduli spaces of K3 surfaces $M$ equipped with a surjective holomorphic map $\pi:M\to\Pb^1$ with generic fiber a complex torus (e.g., an elliptic fibration). Examples include moduli spaces of such maps…

We give a lattice-theoretic characterization for a manifold of $\mathrm{OG}10$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li-Pertusi-Zhao variety of $\mathrm{OG}10$ type associated to…

We present several Orientifolds of M-Theory on $K_3\times S^1$ by additional projections with respect to the finite abelian automorphism groups of $K_3$. The resulting models correspond to anomaly free theories in six dimensions. We…

We develop Floer theory of Lagrangian torus fibers in compact symplectic toric orbifolds. We first classify holomorphic orbi-discs with boundary on Lagrangian torus fibers. We show that there exists a class of basic discs such that we have…

We construct new smooth solutions to the Hull-Strominger system, showing that the Fu-Yau solution on torus bundles over K3 surfaces can be generalized to torus bundles over K3 orbifolds. In particular, we prove that, for $13 \leq k \leq 22$…

The elliptic 3-manifolds are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, that is, those that have finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic…

We compute the $p$-primary components of the linking pairings of orientable 3-manifolds admitting a fixed-point free $S^1$-action. Using this, we show that any non-singular linking pairing on a finite abelian group with homogeneous…

In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each $n \ge 3$ we construct $4$-manifolds $E$ admitting at least $n$ distinct fiberings $p_i: E \to \Sigma_{g_i}$ as a…

We show that the homotopy type of a finite oriented Poincar\'{e} 4-complex is determined by its quadratic 2-type provided its fundamental group is finite and has a dihedral Sylow 2-subgroup. By combining with results of Hambleton-Kreck and…

In the first part of this paper we revisit a classical topological theorem by Tischler (1970) and deduce a topological result about compact manifolds admitting a set of independent closed forms proving that the manifold is a fibration over…

M-theory suggests the study of 11-dimensional space-times compactified on some 7-manifolds. From its intimate relation to superstrings, one possible class of such 7-manifolds are those that have Calabi-Yau threefolds as boundary. In this…

Let $R$ be a closed, oriented topological 4-manifold whose Euler characteristic and signature are denoted by $e$ and $\sigma$. We show that if $R$ has order two $\pi_1$, odd intersection form, and $2e + 3\sigma \geq 0$, then for all but…

Graph manifolds form important classes of $3$-dimensional closed and orientable manifolds. For example, {\it Seifert} manifolds are graph manifolds where hyperbolic manifolds are not. In applying singularity theory of differentiable maps to…

The Clifford torus is a product surface in $\mathbb S^3$ and it is helicoidal. It will be shown that more minimal submanifolds of $\mathbb S^n$ have these properties.

In this paper we construct and classify Lagrangian T^3-fibrations on non compact symplectic manifolds with singular fibres of prescribed topological type. This contributes to the understanding of the structure of the singular fibres that…

Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics whose sectional curvature is locally controlled and whose thick part becomes asymptotically hyperbolic…

We present a systematic study of threefolds fibred by K3 surfaces that are mirror to sextic double planes. There are many parallels between this theory and the theory of elliptic surfaces. We show that the geometry of such threefolds is…

A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami symplectic manifolds, studied by Cannas da Silva, Guillemin…

Closed oriented 4-manifolds with the same geometrically 2-dimensional fundamental group (satisfying certain properties) are classified up to $s$-cobordism by their $w_2$-type, equivariant intersection form and the Kirby-Siebenmann…

The following version of a conjecture of Fischer-Colbrie and Schoen is proved: If M is a complete Riemannian 3-manifold with nonnegative scalar curvature which contains a two-sided torus S which is of least area in its isotopy class then M…