Related papers: Approximate Fibrations in Higher Topos Theory
This paper is a continuation of our paper math.AG/0205321 where we have built a combinatorial model for the torus fibrations of Calabi-Yau toric hypersurfaces. This part addresses the connection between the model torus fibration and the…
Given a semistable fibration $f\colon X\to B$ we introduce a correspondence between foliations $\mathcal{F}$ on $X$ and local systems $\mathbb{L}$ on $B$. Building up on this correspondence we find conditions that give maximal rationally…
We introduce the notion of a good map between topological spaces: a continuous map $f:X \to Y$ is *good* if for every non-empty irreducible locally closed subset $U \subseteq X$, there exists a non-empty open subset $W \subseteq Y$ such…
There are two methods to study families of conformal theories in the operator formalism. In the first method we begin with a theory and a family of deformed theories is defined in the state space of the original theory. In the other there…
This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
Suppose that $\mathcal F$ is a transversely oriented, codimension one foliation of a connected, closed, oriented 3-manifold. Suppose also that $\mathcal F$ has continuous tangent plane field and is {\sl taut}; that is, closed smooth…
This paper undertakes a study of the structure of the fibers of the Chevalley exponentiation maps $f_{(i_1,\dots ,i_d)}$. The fibers of these maps $f_{(i_1,\dots ,i_d)}$ encode the nonnegative real relations amongst exponentiated Chevalley…
Approximate lattices are aperiodic generalisations of lattices of locally compact groups that were first studied in seminal work of Yves Meyer. They are defined as those uniformly discrete approximate subgroups (symmetric subsets stable…
The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and…
We prove that the existence of a Hurewicz fibration between certain spaces with the homotopy type of a CW-complex implies some topological restrictions on their universal coverings. This result is used to deduce differentiable and metric…
We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…
The main purpose this work is to study the minimal fixed point set of fiber-preserving maps for spaces which are fiber bundles over the circle and the fiber is the torus. Using the one-parameter fixed point theory is possible to describe…
In this work we provide a model-independent notion of local fibrations of $(\infty,2)$-categories which generalises the well-known theory of locally coCartesian fibrations of $(\infty,1)$-categories. Based on previous work, we construct a…
We characterize Forman curvature lower bounds via contractivity of the Hodge Laplacian semigroup. We prove that Ollivier and Forman curvature coincide on edges when maximizing the Forman curvature over the choice of 2-cells. To this end, we…
The Hopf index, a topological invariant that quantifies the linking of preimage fibers, is fundamental to the structure and stability of hopfions. In this work, we propose a new mathematical framework for modeling hopfions with high Hopf…
We describe a new relation between the topology of hypersurface complements, Milnor fibers and degree of gradient mappings. In particular we show that any projective hypersurface has affine parts which are bouquets of spheres. The main…
This paper is devoted to the estimation of the number of points of bounded height on fibrations in toric varieties over algebraic varieties, generalizing previous work by Strauch and the second author. Under reasonable hypotheses on…
We introduce new foundations for relative topos theory based on stacks. One of the central results in our theory is an adjunction between the category of toposes over the topos of sheaves on a given site $({\mathcal{C}}, J)$ and that of…
The 102581 flat toric elliptic fibrations over P^2 are identified among the Calabi-Yau hypersurfaces that arise from the 473800776 reflexive 4-dimensional polytopes. In order to analyze their elliptic fibration structure, we describe the…