Related papers: Homotopy classes of maps between Knaster continua

We prove a claim by Williams that the coassembly map is a homotopy limit map. As an application, we show that the homotopy limit map for the coarse version of equivariant $A$-theory agrees with the coassembly map for bivariant $A$-theory…

Let $M$ be an $n$-dimensional compact connected manifold with boundary, $\kappa>0$ a constant and $1\leq q\leq n-1$ an integer. We prove that $M$ supports a Riemannian metric with the interior $q$-curvature $K_q\geq -q\kappa^2$ and the…

We give a model-independent definition of limits for diagrams valued in an $(\infty,n)$-category. We show that this definition is compatible with the existing notion of homotopy 2-limits for 2-categories, with the existing notion of…

Suppose that $X$ and $Y$ are surfaces of finite topological type, where $X$ has genus $g\geq 6$ and $Y$ has genus at most $2g-1$; in addition, suppose that $Y$ is not closed if it has genus $2g-1$. Our main result asserts that every…

If P \to X is a topological principal K-bundle and \hat K a central extension of K by Z, then there is a natural obstruction class \delta_1(P) in \check H^2(X,\uline Z) in sheaf cohomology whose vanishing is equivalent to the existence of a…

We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of…

A bounded curvature path is a continuously differentiable piecewise $C^2$ path with a bounded absolute curvature that connects two points in the tangent bundle of a surface. In this work, we analyze the homotopy classes of bounded curvature…

We construct examples of $S^1$-manifolds with finite second homotopy group and non-vanishing $\hat A$-genus. This is related to the classification of positive quaternionic Kaehler manifolds.

Let $H$ and $F$ be two H\'{e}non maps with biholomorphically equivalent escaping sets, then there exist affine automorphisms $A_1$ and $A_2$ in $\mathbb{C}^2$ such that \[ F=A_1\circ H \circ A_2 \] in $\mathbb{C}^2$.

In this paper we introduce two $1/\kappa^{n}$-type ($n\ge1$) curvature flows for closed convex planar curves. Along the flows the length of the curve is decreasing while the enclosed area is increasing. And finally, the evolving curves…

We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.

We discuss entropy bounds for a class of two-dimensional gravity models. While the Bekenstein bound can be proved to hold in general for weakly gravitating matter, the analogous of the holographic bound is not universal, but depends on the…

In the seminal monograph "Theory of retracts", Borsuk raised the following question: suppose two compact ANR's are $h$--equal, i.e. mutually homotopy dominate each other, are they homotopy equivalent? The current paper approaches this…

We compute the first and second homotopy groups of a class of contact toric manifolds in terms of the images of the associated moment map.

We consider an entropy-type invariant which measures the polynomial volume growth of submanifolds under the iterates of a map, and we establish sharp uniform lower bounds of this invariant for the following classes of symplectomorphisms of…

Let $ R$ be a compact Riemann surface, and let $ P: R \to \mathbb P^1(\mathbb C) $ and $ Q: R \to \mathbb P^1(\mathbb C) $ be holomorphic maps. In this paper, we investigate the following problem: under what conditions do the preimages $…

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic…

We show that for any k>1, stratified sets of finite complexity are insufficient to realize all homology classes of codimension k in all smooth manifolds. We also prove a similar result concerning smooth generic maps whose double-point sets…

In this paper, we establish a second main theorem for holomorphic maps with finite growth index on complex discs intersecting arbitrary families of hypersurfaces (fixed and moving) in projective varieties, which gives an above bound of the…

Given a strong homotopy pushout cube of spaces A, we measure how far it is from also being a homotopy pullback cube. Explicitly, letting P be the homotopy colimit of the diagram obtained from A by forgetting the initial vertex…