Related papers: Sphere eversions and realization of mappings

A strategy for constructing an embedded sphere in a 4-manifold realizing a given homology class which has been successfully applied in the past is to represent the class as a first step stably by an embedded sphere, i.e. after adding…

An obstruction theory for representing homotopy classes of surfaces in 4-manifolds by immersions with pairwise disjoint images is developed, using the theory of non-repeating Whitney towers. The accompanying higher-order intersection…

In this paper we use character variety methods to study homomorphisms between the fundamental groups of 3-manifolds, in particular those induced by non-zero degree maps. A {\it knot manifold} is a compact, connected, irreducible, orientable…

We study complete, finite volume $n$-manifolds $M$ of bounded nonpositive sectional curvature. A classical theorem of Gromov says that if such $M$ has negative curvature then it is homeomorphic to the interior of a compact…

N. V. Efimov \cite{Ef1} proved that there is no complete, smooth surface in $\R^3$ with uniformly negative curvature. We extend this to isometric immersions in a 3-manifold with pinched curvature: if $M^3$ has sectional curvature between…

Special generic maps are smooth maps between smooth manifolds with only definite fold points as their singularities. The problem of whether a closed $n$-manifold admits a special generic map into Euclidean $p$-space for $1 \leq p \leq n$…

We study a notion of strict pseudoconvexity in the context of topologically (often unsmoothably) embedded 3-manifolds in complex surfaces. Topologically pseudoconvex (TPC) 3-manifolds behave similarly to their smooth analogues, cutting out…

We prove that any steady solution to the real analytic Euler equations on a Riemannian 3-sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an extension of Fomenko's work on the topology of integrable…

This article concerns a question asked by M. V. Nori on homotopy of sections of Projective modules defined on the polynomial algebra over a smooth affine domain $R$. While this question has an affirmative answer, it is known that the…

We study time and space equivariant wave maps from $M\times\RR\rightarrow S^2,$ where $M$ is diffeomorphic to a two dimensional sphere and admits an action of SO(2) by isometries. We assume that metric on $M$ can be written as…

We consider $\mathcal{A}$-finite map germs $f$ from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{2n},0)$. First, we show that the number of double points that appears in a stabilization of $f$, denoted by $d(f)$, can be calculated as the length of…

We extend our previous analysis of Riemannian four-manifolds M admitting rigid supersymmetry to N=1 theories that do not possess a U(1)_R symmetry. With one exception, we find that M must be a Hermitian manifold. However, the presence of…

Let $M$ be a connected, non-compact $m$-dimensional Riemannian manifold. In this paper we consider smooth maps $\phi: M \to \mathbb{R}^n$ with images inside a non-degenerate cone. Under quite general assumptions on $M$, we provide a lower…

An example of a finite dimensional factorizable ribbon Hopf C-algebra is given by a quotient H=u_q(g) of the quantized universal enveloping algebra U_q(g) at a root of unity q of odd degree. The mapping class group M_{g,1} of a surface of…

We investigate the realisability of the Casson-Sullivan invariant for homeomorphisms of smooth $4$-manifolds, which is the obstruction to a homeomorphism being stably pseudo-isotopic to a diffeomorphism, valued in the third cohomology of…

We show a sharp and rigid spectral generalization of the classical Bishop--Gromov volume comparison theorem: if a closed Riemannian manifold $(M,g)$ of dimension $n\geq3$ satisfies $$…

We prove that the metric of the Riemannian product $(\mb{S}^k(r_1)\times \mb{S}^{n-k}(r_2), g^n_k)$, $r_1^2+r_2^2=1$, is a Yamabe metric in its conformal class if, and only if, either $g^n_k$ is Einstein, or the linear isometric embedding…

Let A be a based subspace of Y. Under the assumptions that Y is path-connected and that the reduced diagonal map of A induces the zero map in all mod 2 reduced homology groups, we compute a formula for the mod 2 reduced Poincar\'{e} series…

In 1962, Wall showed that smooth, closed, oriented, $(n-1)$-connected $2n$-manifolds of dimension at least $6$ are classified up to connected sum with an exotic sphere by an algebraic refinement of the intersection form which he called an…

Let $L_0,L_1,L_2 \subset M$ be exact Lagrangian spheres in a Liouville domain $M$ with $2c_1(M)=0$. If $L_0,L_1,L_2$ form an $A_3$-configuration, we show that $\mathscr{L}(L_0)$ and $\mathscr{L}(L_2)$ endowed with the Hofer metric contain…