Related papers: Evaluation Maps in Rational Homotopy

We survey research on the homotopy theory of the space map(X, Y) consisting of all continuous functions between two topological spaces. We summarize progress on various classification problems for the homotopy types represented by the…

Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the…

Structural properties of finite digraphs $R$ and $S$ are studied which enforce $\# {\cal H}(G,R) \leq \# {\cal H}(G,S)$ for every finite digraph $G \in \mathfrak{ D }'$, where ${\cal H}(G,H)$ is the set of homomorphisms from $G$ to $H$, and…

The paper addresses the question whether a random functional, a map from a set $E$ into the space of real-valued measurable functions on a probability space, has a measurable version with values in ${\mathbb R}^E$. Similarly, one may ask…

Let X be a complex nonsingular affine algebraic variety, K a holomorphically convex subset of X, and Y a homogeneous variety for some complex linear algebraic group. We prove that a holomorphic map f:K-->Y can be uniformly approximated on K…

A free homotopy decomposition of any continuous map from a compact Riemmanian manifold $\mathcal{M}$ to a compact Riemannian manifold $\mathcal{N}$ into a finite number maps belonging to a finite set is constructed, in such a way that the…

Let $G$ be a cyclic $p$-group or generalized quaternion group, $X\in \pi_0 S_G$ be a virtual $G$-set, and $V$ be a fixed point free complex $G$-representation. Under conditions depending on the sizes of $G$, $X$, and $V$, we construct a…

We construct and study a functorial extension of the evaluation map $S^1 \times \mathcal{L} X \to X$ to transfers along finite covers. For finite covers of classifying spaces of finite groups, we provide algebraic formulas for this…

This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…

Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of…

Let p be a singular point of a variety. Consider a resolution where the preimage of p is a simple normal crossing divisor E. The combinatorial structure of E is described by a cell complex D(E), called the dual graph or dual complex of E.…

Let X and Y be finite nilpotent CW complexes with dimension of X less than the connectivity of Y. Generalizing results of Vigu\'e-Poirrier and Yamaguchi, we prove that the mapping space Map(X,Y) is rationally formal if and only if Y has the…

In "Generalized Group Characters and Complex Oriented Cohomology Theories", Hopkins, Kuhn, and Ravenel develop a way to study cohomology rings of the form E^*(BG) in terms of a character map. The character map can be interpreted as a map of…

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…

Let X denote either CP^m or C^m. We study certain analytic properties of the space E^n of ordered geometrically generic n-point configurations in X. This space consists of all q=(q_1,...,q_n) in X^n such that no m+1 of the points…

Let $G$ be a simple and simply connected algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p>0$. Assume that $p$ is good for the root system of $G$ and that the covering map $G_{sc} \rightarrow G$ is separable.…

We give a brief survey on the entropy of holomorphic self maps $f$ of compact K\"ahler manifolds, and rational dominating self maps $f$ of smooth projective varieties. We emphasize the connection between the entropy and the spectral radii…

For a pointed topological space $X$, we use an inductive construction of a simplicial resolution of $X$ by wedges of spheres to construct a "higher homotopy structure" for $X$ (in terms of chain complexes of spaces). This structure is then…

Let X be a compact nonsingular real algebraic variety. We prove that if a continuous map from X into the unit p-sphere is homotopic to a continuous rational map, then, under certain assumptions, it can be approximated in the compact-open…

It is a deep fact that the homotopy classification of topological manifolds is convariantly functorial. In other words, a map from a topological manifold M to another N naturally induces a map from the structure set S(M) to S(N). We extend…