Related papers: A space level light bulb theorem in all dimensions

We prove a result analogous to Reeb's theorem in the context of Morse-Bott functions: if a closed, smooth manifold $M$ admits a Morse-Bott function having two critical submanifolds $S^k$ and $S^l$ ($k \neq l$), then $M$ has dimension…

We classify four-dimensional manifolds endowed with symplectic pairs admitting embedded symplectic spheres with non-negative self-intersection, following the strategy of McDuff's classification of rational and ruled symplectic four…

We prove that the group of area-preserving diffeomorphisms of the 2-sphere admits a non-trivial homogeneous quasimorphism to the real numbers with the following property. Its value on any diffeomorphism supported in a sufficiently small…

We show that the discretized configuration space of $k$ points in the $n$-simplex is homotopy equivalent to a wedge of spheres of dimension $n-k+1$. This space is homeomorphic to the order complex of the poset of ordered partial partitions…

In this paper, we use normal surface theory to study Dehn filling on a knot-manifold. First, it is shown that there is a finite computable set of slopes on the boundary of a knot-manifold that bound normal and almost normal surfaces in a…

It is proved that any smooth manifold $\mathcal M$ of dimension $m$ admits a smooth polynomially convex embedding into $\mathbb C^n$ when $n\geq \lfloor 5m/4\rfloor$. Further, such embeddings are dense in the space of smooth maps from…

Let M be a compact 3-manifold whose interior admits a complete hyperbolic structure. We let Lambda(M) be the supremum of the bottom eigenvalue of the Laplacian of N, where N varies over all hyperbolic 3-manifolds homeomorphic to the…

We use pinched smooth hyperbolization to show that every closed, nonpositively curved $n$-dimensional manifold $M$ can be embedded as a totally geodesic submanifold of a closed, nonpositively curved $(n+1)$-dimensional manifold $\hat{M}$ of…

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…

We determine loop space decompositions of simply-connected four-manifolds, $(n-1)$-connected $2n$-dimensional manifolds provided $n\notin\{4,8\}$, and connected sums of products of two spheres. These are obtained as special cases of a more…

We prove that in Euclidean space $R^{n+1}$ any compact immersed nonnegatively curved hypersurface $M$ with free boundary on the sphere $S^n$ is an embedded convex topological disk. In particular, when the $m^{th}$ mean curvature of $M$ is…

We prove that there is an algorithm which determines whether or not a given 2-polyhedron can be embedded into some integral homology 3-sphere. This is a corollary of the following main result. Let $M$ be a compact connected orientable…

We generalise theorems of Khodorovskiy and Park-Park-Shin, and give new topological proofs of those theorems, using embedded surfaces in the 4-ball and branched double covers. These theorems exhibit smooth codimension-zero embeddings of…

It is conjectured since long that for any convex body $K \subset \mathbb{R}^n$ there exists a point in the interior of $K$ which belongs to at least $2n$ normals from different points on the boundary of $K$. The conjecture is known to be…

Let $LHT$ be a left handed trefoil knot and $K$ be any knot. We define $M_n(K)$ to be the homology $3$-sphere which is represented by a simple link of $LHT$ and $LHT \sharp K$ with framings $0$ and $n$ respectively. Starting with this link,…

Here are two of our main results: Theorem 1. Let X be a normal space with dim X=n and m\geq n+1. Then the space C*(X,R^m) of all bounded maps from X into R^m equipped with the uniform convergence topology contains a dense G_{\delta}-subset…

Directed Algebraic Topology is beginning to emerge from various applications. The basic structure we shall use for such a theory, a 'd-space', is a topological space equipped with a family of 'directed paths', closed under some operations.…

We study the space of oriented genus g subsurfaces of a fixed manifold M, and in particular its homological properties. We construct a "scanning map" which compares this space to the space of sections of a certain fibre bundle over M…

We analyze the class of Generalized Double Semion (GDS) models in arbitrary dimensions from the point of view of lattice Hamiltonians. We show that on a $d$-dimensional spatial manifold $M$ the dual of the GDS is equivalent, up to constant…

We prove that for any two lattices $L, M \subseteq \mathbb{R}^d$ of the same volume there exists a measurable, bounded, common fundamental domain of them. In other words, there exists a bounded measurable set $E \subseteq \mathbb{R}^d$ such…