Related papers: Complexes equivalent to $S^{2k-1}$-fibrations over…

For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are…

Waldhausen's $S_\bullet$-construction gives a way to define the algebraic $K$-theory space of a category with cofibrations. Specifically, the $K$-theory space of a category with cofibrations $\mathcal{C}$ can be defined as the loop space of…

We consider, in flux compactification of heterotic string theory, spacetime-filling five-branes. Stabilizing the fivebrane involves minimizing the combined energy density of the tension and a Coulomb potential associated with an internal…

We define extension $\infty$-categories for exact $\infty$-categories in terms of bifibrations. Extension $\infty$-categories are invariant when passing to the stable hull, and consequently we show that they form an $\Omega$-spectrum,…

A space $X$ is "sequentially $n$-connected" at $x\in X$ if for every $0\leq k\leq n$ and sequence of maps $f_1,f_2,f_3,\dots:S^k\to X$ that converges toward a point $x\in X$, the maps $f_m$ contract by a sequence of null-homotopies that…

This article introduces descriptive cellular homology on cell complexes, which is an extension of J.H.C. Whitehead's CW topology. A main result is that a descriptive cellular complex is a topology on fibres in a fibre bundle. An application…

We prove that the group of homotopy classes of relative homotopy automorphisms of a simply connected finite CW-complex is finitely presented and that the rationalization map from this group to its rational analogue has a finite kernel.

We prove that completion at a set of primes preserves homotopy fibre squares of connected nilpotent spaces. As a consequence, we deduce the Hasse fracture square associated to a connected nilpotent space. Along the way, we give a quick…

In this paper we consider a diffeomorphism $f$ of a compact manifold $M$ which contracts an invariant foliation $W$ with smooth leaves. If the differential of $f$ on $TW$ has narrow band spectrum, there exist coordinates $H _x:W_x\to T_xW$…

Let $M$ denote a two-dimensional Moore space (so $H_2(M; \Z) = 0$), with fundamental group $G$. The $M$-cellular spaces are those one can build from $M$ by using wedges, push-outs, and telescopes (and hence all pointed homotopy colimits).…

We use Richter's $2$-primary proof of Gray's conjecture to give a homotopy decomposition of the fibre $\Omega^3S^{17}\{2\}$ of the $H$-space squaring map on the triple loop space of the $17$-sphere. This induces a splitting of the mod-$2$…

In this paper we consider classifying spaces of a family of $p$-groups and we prove that mod $p$ cohomology enriched with Bockstein spectral sequences determines their homotopy type among $p$-completed CW-complexes. We end with some…

We classify exterior fibrations in the exterior homotopy category. As a result we also classify proper fibrations between CW-complexes.

We consider real spectra, collections of Z/(2)-spaces indexed over Z oplus Z alpha with compatibility conditions. We produce fibrations connecting the homotopy fixed points and the spaces in these spectra. We also evaluate the map which is…

This paper is devoted to the study of the knot Floer homology groups HFK(S^3,K_{2,n}), where K_{2,n} denotes the (2,n) cable of an arbitrary knot, K. It is shown that for sufficiently large |n|, the Floer homology of the cabled knot depends…

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…

Given a commutative ring $R$ and finitely generated ideal $I$, one can consider the classes of $I$-adically complete, $L_0^I$-complete and derived $I$-complete complexes. Under a mild assumption on the ideal $I$ called weak pro-regularity,…

In this paper we give a very natural description of the bijections between the minimal CW-complex homotopy equivalent to the complement of a supersolvable arrangement $\mathcal{A}$, the $\textbf{nbc}$ basis of the Orlik-Solomon algebra…

In this paper we show that the cohomology of a connected CW complex is periodic if and only if it is the base space of an orientable spherical fibration with total space that is homotopically finite dimensional. As applications we…

Let G be a finite group given in one of the forms listed in the title with period 2d and X(n) an n-dimensional CW-complex with the homotopy type of an n-sphere. We study the automorphism group Aut(G) to compute the number of distinct…