相关论文: Embeddings of non-simply-connected 4-manifolds in …

We work in the smooth category. Let $N$ be a closed connected orientable 4-manifold with torsion free $H_1$, where $H_q:=H_q(N;Z)$. Our main result is a complete readily calculable classification of embeddings $N\to R^7$, up to the…

Let N be a closed, connected, smooth 4-manifold with H_1(N;Z)=0. Our main result is the following classification of the set E^7(N) of smooth embeddings N->R^7 up to smooth isotopy. Haefliger proved that the set E^7(S^4) with the connected…

We work in the smooth category. Let N be a closed connected n-manifold and assume that m>n+2. Denote by E^m(N) the set of embeddings N -> R^m up to isotopy. The group E^m(S^n) acts on E^m(N) by embedded connected sum of a manifold and a…

We work in the smooth category. If there are knotted embeddings S^n\to R^m, which often happens for 2m<3n+4, then no concrete complete description of embeddings of n-manifolds into R^m up to isotopy was known, except for disjoint unions of…

We develop a new approach to the classical problem on isotopy classification of embeddings of manifolds into Euclidean spaces. This approach involves studying of a new embedding invariant, of almost-embeddings and of smoothing, as well as…

We obtain estimations for isotopy classes of embeddings of closed k-connected n-manifolds into R^{2n-k-1} for n>2k+5 and k\ge0. This is done in terms of an exact sequence involving the Whitney invariants and an explicitly constructed action…

Given a closed four-manifold $X$ with an indefinite intersection form, we consider smoothly embedded surfaces in $X \setminus $int$(B^4)$, with boundary a knot $K \subset S^3$. We give several methods to bound the genus of such surfaces in…

The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and to provide a reference for the topology of…

We compute in many classes of examples the first potentially interesting homotopy group of the space of embeddings of either an arc or a circle into a manifold $M$ of dimension $d\geq4$. In particular, if $M$ is a simply connected…

We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper…

To a smooth, compact, oriented, properly-embedded surface in the $4$-ball, we define an invariant of its boundary-preserving isotopy class from the Khovanov homology of its boundary link. Previous work showed that when the boundary link is…

We define an isotopy invariant of embeddings N -> R^m of manifolds into Euclidean space. This invariant together with the \alpha-invariant of Haefliger-Wu is complete in the dimension range where the \alpha-invariant could be incomplete. We…

Let $M_1$ and $M_2$ be closed connected orientable $3$-manifolds. We classify the sets of smooth and piecewise linear isotopy classes of embeddings $M_1\sqcup M_2\rightarrow S^6$.

In this article, we propose a new approach for describing and understanding knots and links in a 3-manifold through the use of an embedded non-orientable surface. Specifically, we define a plat-like representation based on this…

We classify nonnegatively curved simply connected 4-manifolds with circle symmetry up to equivariant diffeomorphisms. The main problem is rule out knotted curves in the singular set of the orbit space. As an extension of this work we…

This article is concerned with locally flatly immersed surfaces in simply-connected $4$-manifolds where the complement of the surface has fundamental group $\mathbb{Z}$. Once the genus and number of double points are fixed, we classify such…

Suppose that $N_1$ and $N_2$ are closed smooth manifolds of dimension $n$ that are homeomorphic. We prove that the spaces of smooth knots $Emb(S^1, N_1)$ and $Emb(S^1, N_2)$ have the same homotopy $(2n-7)$-type. In the 4-dimensional case…

We study the classification of closed, smooth, spin, $1$-connected $7$-manifolds whose integral cohomology ring is isomorphic to $H^*(\mathbb{C}P^2\times S^3)$. We also prove that if the integral cohomology ring of a closed, smooth, spin,…

For a smooth manifold $N$ denote by $E^m(N)$ the set of smooth isotopy classes of smooth embeddings $N\to\mathbb R^m$. A description of the set $E^m(S^p\times S^q)$ was known only for $p=q=0$ or for $p=0$, $m\ne q+2$ or for $2m\ge…

We study continuous embeddings of the long line L into L^n (n>1) up to ambient isotopy of L^n. We define the direction of an embedding and show that it is (almost) a complete invariant in the case n=2 for continuous embeddings, and in the…