Related papers: Embeddings of submanifolds and normal bundles

We obtain smooth M-theory solutions whose geometry is a warped product of AdS_5 and a compact internal space that can be viewed as an S^4 bundle over S^2. The bundle can be trivial or twisted, depending on the even or odd values of the two…

In this article we present a coherent rigorous overview of the main properties of Sobolev-Slobodeckij spaces of sections of vector bundles on compact manifolds; results of this type are scattered through the literature and can be difficult…

In this paper, we study the embedding problem of homogeneous quandles. We give a necessary and sufficient condition under which a quandle homomorphism from the homogeneous quandle associated with a quandle triplet $(G,H,\sigma)$ into a…

We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the configuration space of a metric space and develop tools to…

The generalized Miller-Morita-Mumford classes of a manifold bundle with fiber $M$ depend only on the underlying $\tau_M$-fibration, meaning the family of vector bundles formed by the tangent bundles of the fibers. This motivates a closer…

Let M and N be smooth manifolds without boundary. Immersion theory suggests that an understanding of the space of smooth embeddings emb(M,N) should come from an analysis of the cofunctor V |--> emb(V,N) from the poset O of open subsets of M…

For each integer q>0 there is a cohomology theory such that the zero cohomology group of a manifold N of dimension n is a certain group of cobordism classes of proper fold maps of manifolds of dimension n+q into N. We prove a splitting…

For a compact 3-manifold $M$ which is a circle bundle over a compact Riemann surface $\Sigma$ with even Euler number $e(M)$, and with a Riemannian metric compatible with the bundle projection, there exists a compact minimal surface $S$ in…

The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are general. Studies of this type is fundamental and important. They…

We classify smooth complex projective varieties $X \subset \proj^N$ of dimension $2s+1$ containing a linear subspace $\Lambda$ of dimension $s$ whose normal bundle $N_{\Lambda/X}$ is numerically effective.

In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the well-known Muckenhoupt A_p-condition. Sufficient conditions for boundedness and compactness of the embedding operators are obtained for…

We introduce the notion of coupled embeddability, defined for maps on products of topological spaces. We use known results for nonsingular biskew and bilinear maps to generate simple examples and nonexamples of coupled embeddings. We study…

Let $M$ be a submanifold of ${\Bbb P}^N$ of dimension $n>2$. Suppose that $(M,{\Cal O}_M(1))\cong{\Bbb P}({\Cal E}),{\Cal O}(1))$ for some vector bundle ${\Cal E}$ on a surface $S$. Then $N\ge 2n-1$ by Barth-Lefschetz Theorem. We are…

Given Poincare spaces M and X, we study the possibility of compressing embeddings of M x I in X x I down to embeddings of M in X. This results in a new approach to embedding in the metastable range both in the smooth and Poincare duality…

We investigate constraints on embeddings of a non-orientable surface in a $4$-manifold with the homology of $M \times I$, where $M$ is a rational homology $3$-sphere. The constraints take the form of inequalities involving the genus and…

We construct persistent bundles over configuration spaces of hard spheres and use the characteristic classes of these persistent bundles to give obstructions for embedding problems. The configuration spaces of $k$-hard spheres ${\rm…

We give geometric formulae which enable us to detect (completely in some cases) the regular homotopy class of an immersion with trivial normal bundle of a closed oriented 3-manifold into 5-space. These are analogues of the geometric…

We classify immersions $f$ of $S^1$ in a $2$-manifold $M$ in terms of elementary invariants: the parity $S(f)$ of the number of double points of a self-transverse $C^1$-approximation of $f$, and the turning number $T(e\bar f)$ of the…

Recently Galatius, Madsen, Tillmann and Weiss identified the homotopy type of the classifying space of the cobordism category of embedded d-dimensional manifolds [7] for each positive integer d. Their result lead to a new proof of the…

Let $(X,J) $ be an almost complex manifold with a (smooth) involution $\sigma:X\to X$ such that fix($\sigma$) is non-empty. Assume that $\sigma$ is a complex conjugation, i.e, the differential of $\sigma$ anti-commutes with $J$. The space…