Related papers: Obstructions for constructing equivariant fibratio…

We consider fibrations by affine lines on smooth affine surfaces obtained as complements of smooth rational curves $B$ in smooth projective surfaces $X$ defined over an algebraically closed field of characteristic zero. We observe that…

We develop an obstruction theory for homotopy of homomorphisms f,g : M -> N between minimal differential graded algebras. We assume that M = Lambda V has an obstruction decomposition given by V = V_0 oplus V_1 and that f and g are homotopic…

We show that the moduli space of all smooth fibrations of a three-sphere by simple closed curves has the homotopy type of a disjoint union of a pair of two-spheres if the fibers are oriented, and of a pair of real projective planes if…

We study fibrations in the category of cubespaces/nilspaces. We show that a fibration of finite degree $f \colon X\rightarrow Y$ between compact ergodic gluing cubespaces (in particular nilspaces) factors as a (possibly countable) tower of…

For a weakly branch group $G$ acting on a regular enough rooted tree, we provide two constructions of continuous families of distinct subgroups that are not closed in the profinite topology on $G$. On the one hand, we construct a continuous…

The orbifold construction $A\mapsto A^G$ for a finite group $G$ is fundamental in rational conformal field theory. The construction of $Rep(A^G)$ from $Rep(A)$ on the categorical level, often called gauging, is also prominent in the study…

We provide a necessary and sufficient condition for the derived self-intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme. As a consequence we deduce a generalized HKR isomorphism. We also…

We study algebraic conditions on a group G under which every properly discontinuous, isometric G-action on a Hadamard manifold has a G-invariant Busemann function. For such G we prove the following structure theorem: every open complete…

This paper studies the (small) quantum homology and cohomology of fibrations $p: P\to S^2$ whose structural group is the group of Hamiltonian symplectomorphisms of the fiber $(M,\om)$. It gives a proof that the rational cohomology splits…

Let $G$ be a reductive complex Lie group acting holomorphically on Stein manifolds $X$ and $Y$. Let $p_X\colon X\to Q_X$ and $p_Y\colon Y\to Q_Y$ be the quotient mappings. When is there an equivariant biholomorphism of $X$ and $Y$? A…

The familiar construction of categories of fractions, due to Gabriel and Zisman, allows one to invert a class W of arrows in a category in a universal way. Similarly, bicategories of fractions allow one to invert a collection of arrows in a…

This article is devoted to the investigation of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. These groups are…

Gerbes are locally connected presheaves of groupoids. They are classified up to local weak equivalence by path components in a 2-cocycle category taking values in all sheaves of groups, their isomorphisms and homotopies. If F is a full…

Let $F\hookrightarrow E\twoheadrightarrow B$ be a fibration whose base space $B$ is a finite simply-connected CW-complex of dimension $\leq p$ and whose total space $E$ is a path-connected CW-complex of dimension $\leq p-1$. If $\alpha\in…

We gather conditions on a class H of continuous maps of topological spaces that allow a reasonable theory of fibrations up to an equivalence (a map from this class) which we call H-fibrations. The weak homotopy equivalences recover…

Let $1 \to K \longrightarrow G \stackrel{\pi}\longrightarrow Q$ be an exact sequence of hyperbolic groups. Let $Q_1 < Q$ be a quasiconvex subgroup and let $G_1=\pi^{-1}(Q_1)$. Under relatively mild conditions (e.g. if $K$ is a closed…

We study the geometry of the Hitchin fibration for $\mathcal{L}$-valued $G$-Higgs bundles over a smooth projective curve of genus $g$, where $G$ is a reductive group and $\mathcal{L}$ is a suitably positive line bundle. We show that the…

Given a fibration of simply connected CW complexes of finite type, we study the evaluation subgroup of the fibre inclusion as an invariant of fibre-homotopy type. For spherical fibrations, we show the evaluation subgroup may be expressed as…

Given a fiber bundle of GKM spaces, $\pi\colon M\to B$, we analyze the structure of the equivariant $K$-ring of $M$ as a module over the equivariant $K$-ring of $B$ by translating the fiber bundle, $\pi$, into a fiber bundle of GKM graphs…

For any group $G$ of self homotopy equivalences of the finite nilpotent complex $X$, acting nilpotently on its homology, and for any nilpotent subcomplex $A$, we prove that the universal fibration $$ X \longrightarrow B(*,{\rm…