Related papers: Mapping Spaces and Postnikov Invariants

We show that in a fibration the coformality of the base space implies the coformality of the total space under reasonable conditions, and these conditions can not be weakened. The result is partially dual to the classical work of Lupton…

A metric space $M$ us said to have the fibered approximation property in dimension $n$ (br., $M\in \mathrm{FAP}(n)$) if for any $\epsilon>0$, $m\geq 0$ and any map $g: I^m\times I^n\to M$ there exists a map $g':I^m\times I^n\to M$ such that…

Let $B{ aut}_1X$ be the Dold-Lashof classifying space of orientable fibrations with fiber $X$. For a rationally weakly trivial map $f:X\to Y$, our strictly induced map $a_f: (Baut_1X)_0\to (Baut_1Y)_0$ induces a natural map from a…

Our aim is to construct fibrewise localizations in model categories. For pointed spaces, the general idea is to decompose the total space of a fibration as a diagram over the category of simplices of the base and replace it by the localized…

The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle…

We continue to investigate applications of $k$-covers in function spaces with the compact-open topology.

Around 1960, R. Palais and J. Cerf proved a fundamental result relating spaces of diffeomorphisms and imbeddings of manifolds: If V is a submanifold of M, then the map from Diff(M) to Imb(V,M) that takes f to its restriction to V is locally…

The paper is devoted to the problem when a map from some closed connected manifold to an aspherical closed manifold approximately fibers, i.e., is homotopic to Manifold Approximate Fibration. We define obstructions in algebraic K-theory.…

We study an analogue of fibrations of topological spaces with the homotopy lifting property in the setting of C*-algebra bundles. We then derive an analogue of the Leray-Serre spectral sequence to compute the K-theory of the fibration in…

We consider the homotopy type of maps between symplectic surface whose graphs form symplectic submanifolds of the product. We give a purely topological model for this space in terms of maps with constrained numbers of pre-images. We use…

In an earlier paper of Cadek, Vokrinek, Wagner, and the present authors, we investigated an algorithmic problem in computational algebraic topology, namely, the computation of all possible homotopy classes of maps between two topological…

Expanding on the comprehensive factorization of functors internal to a category C, under fairly mild conditions on a monad T on C we establish that this orthogonal factorization system exists even in Burroni's category Cat(T) of (internal)…

A kind of unstable homotopy theory on the category of associative rings (without unit) is developed. There are the notions of fibrations, homotopy (in the sense of Karoubi), path spaces, Puppe sequences, etc. One introduces the notion of a…

We use Gromov's K--area to define a generalized homology theory on compact smooth manifolds. In fact, this theory collects obstructions to the enlargeability of the manifold and its nontrivial submanifolds. Moreover, using the K--area…

Many interesting classes of maps from homotopical algebra can be characterised as those maps with the right lifting property against certain sets of maps (such classes are sometimes referred to as cofibrantly generated). In a more…

Lyubashenko's construction associates representations of mapping class groups Map_{g,n} of Riemann surfaces of any genus g with any number n of holes to a factorizable ribbon category. We consider this construction as applied to the…

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to a new and unexpected result about…

We prove that many spaces of positive scalar curvature metrics have the homotopy type of infinite loop spaces. Our result in particular applies to the path component of the round metric inside $\mathcal{R}^+ (S^d)$ if $d \geq 6$. To achieve…

We present general techniques for constructing functorial factorizations appropriate for model structures that are not known to be cofibrantly generated. Our methods use "algebraic" characterizations of fibrations to produce factorizations…

In this paper we introduce the notion of cofrontal mappings, as the dual objects to frontal mappings, and study their basic local and global properties. Cofrontals are very special mappings and far from generic nor stable except for the…