Related papers: The homotopy sequence for regular singular stratif…
In this article, we consider an infinite family of normal surface singularities with an integral homology sphere link which is related to the family of space monomial curves with a plane semigroup. These monomial curves appear as the…
This work serves as an opening and basis of an ongoing program investigating topological and geometric aspects of the moduli space of smooth fiberings on a manifold. The present paper focuses on the algebraic and differential topology of…
Given a closed simply connected manifold $M$ of dimension $2n\ge6$, we compare the ring of characteristic classes of smooth oriented bundles with fibre $M$ to the analogous ring resulting from replacing $M$ by the connected sum…
Manifolds and fiber bundles, while superficially different, have strong parallels; in particular, they are both defined in terms of equivalence classes of atlases or in terms of maximal atlases, with the atlases treated as mere adjuncts.…
The paper establishes an equivalence between directed homotopy categories of (diagrams of) cubical sets and (diagrams of) directed topological spaces. This equivalence both lifts and extends an equivalence between classical homotopy…
We show that isomorphisms of fundamental groups of elementary anabelian varieties -- varieties obtained as iterated fibrations of hyperbolic curves -- over sub-$p$-adic fields correspond bijectively to isomorphisms of varieties. Moreover,…
We extend the homotopy theories based on point reduction for finite spaces and simplicial complexes to finite acyclic categories and $\Delta$-complexes, respectively. The functors of classifying spaces and face posets are compatible with…
The James fibrations give rise to the geometric EHP sequences of homotopy groups of spheres. Using techniques from the Lambda algebra, \cite{BCKQRS66} shows that there are similar long exact sequences of Ext groups defining the $E_{2}-$page…
We apply our earlier work on the higher-dimensional analogue of the Mumford conjecture to two questions. Inspired by work of Ebert we prove non-triviality of certain characteristic classes of bundles of smooth closed manifolds. Inspired by…
Given a compact complex manifold $M$, we investigate the holomorphic vector bundles $E$ on $M$ such that $\varphi^* E$ is trivial for some surjective holomorphic map $\varphi$, to $M$, from some compact complex manifold. We prove that these…
In this note we explain that homotopy coherent simplicial nerve has to used intead of the standard definition in the author's papers on formal deformation theory. A convenient version of the notion of fibered category is presented which is…
This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from…
In this paper, we prove that certain spherical fibrations over certain CW-complexes are stably fibre homotopy equivalent to $\mm{TOP}$-spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for…
Let P be a connected smooth p-manifold. We describe the group of all cobordism classes of smooth maps of n-manifolds to P with singularities of a given $cal K$-invariant class in terms of certain stable homotopy groups by applying the…
In this paper, we construct a seven-term exact sequence involving the cohomology groups of a group extension. Although the existence of such a sequence can be derived using spectral sequence arguments, there is little knowledge about some…
A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of ``gauge fields'' (sections…
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…
In this article we apply ideas from homotopy theory to the study of singular foliations. We verify that a technical lemma remains valid for left semi-model categories. When applied to the category of $L_\infty$-algebroids thanks to the work…
We provide a simple condition on rational cohomology for the total space of a pullback fibration over a connected sum to have the rational homotopy type of a connected sum, after looping. This takes inspiration from recent work of Jeffrey…
We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in…