Related papers: $\pi_1$-injective proper maps between non-compact …

In this paper we study the set of projective maps between compact proper convex real projective manifolds. We show that this set contains only finitely many distinct homotopy classes and each homotopy class has the structure of a real…

We classify all tight holomorphic maps between Hermitian symmetric spaces of non-compact type.

A map between connected $2$-manifolds has a geometric kernel if it sends a non-contractible simple loop to a null-homotopic loop. While every non-$\pi_1$-injective map between compact surfaces admits a geometric kernel, this generally fails…

We show that every orientable infinite-type surface is properly rigid as a consequence of a more general result. Namely, we prove that if a homotopy equivalence between any two non-compact orientable surfaces is a proper map, then it is…

We describe the relation of $r$-similarity and finite-order invariants on the homotopy set $[S^1,Y]=\pi_1(Y)$.

We prove the existence of lattice isomorphic line arrangements having $\pi_1$-equivalent or homotopy-equivalent complements and non homeomorphic embeddings in the complex projective plane. We also provide two explicit examples, one is…

Motivated by the recent work of Algom-Kfir and Bestinva introducing the mapping class group of an infinite graph via proper homotopy equivalences, we give a necessary and sufficient condition for a surface to be properly homotopy equivalent…

A standard fact about two incompressible surfaces in an irreducible 3-manifold is that one can move one of them by isotopy so that their intersection becomes $\pi_1$-injective. By extending it on the maps of some 3-dimensional…

We show that every continuous map from one translationally finite tiling space to another can be approximated by a local map. If two local maps are homotopic, then the homotopy can be chosen so that every interpolating map is also local.

We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…

We show that the pure mapping class group is uniformly perfect for a certain class of infinite type surfaces with noncompact boundary components. We then combine this result with recent work in the remaining cases to give a complete…

We show that all self-maps of non-zero degree of $3$-manifolds not covered by $S^3$ and of Thurston geometric $4$-manifolds and their connected sums not covered by $N\#(\#_{p\geq0}S^2\times S^2)\#(\#_{q\geq0}\mathbb C P^2)$, where $N$ is an…

Immersions of graphs to the projective plane are studied. A classification of immersions up to regular homotopy is given. A complete invariant of immersions up to regular homotopy is constructed. Equivalence classes are described.

We examine maps between noncommutative projective spaces. A surjection of graded rings A-->A/J induces a closed immersion Proj(A/J)-->Proj(A). A homomorphism f:A-->B between graded rings induces an affine map U --> Proj(A) from a non-empty…

We characterize locally injective semialgebraic maps between two semialgebraic sets in terms of the induced homomorphism between their rings of (continuous) semialgebraic functions.

We prove that a proper holomorphic map between two bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the…

In the paper, we consider the harmonic maps between surfaces $\Sigma$ and $S$ in the homotopy class of a (branched) covering map $u_0$. We prove the uniqueness of critical points of energy function and the injectivity of Hopf differential…

Let $S$ be a complete flat surface, such as the Euclidean plane. We determine the homeomorphism class of the space of all curves on $S$ which start and end at given points in given directions and whose curvatures are constrained to lie in a…

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…

We show that a homotopy equivalence between two non-compact orientable surfaces is homotopic to a homeomorphism if and only if it preserves the Goldman bracket, provided our surfaces are neither the plane nor the punctured plane.