相关论文: Moment-angle manifolds and connected sums of spher…

Let $E$ be the Whitney sum of complex line bundles over a topological space $X$. Then, the projectivization $P(E)$ of $E$ is called a \emph{projective bundle} over $X$. If $X$ is a non-singular complete toric variety, so is $P(E)$. In this…

In this paper we show that any good toric contact manifold has well defined cylindrical contact homology and describe how it can be combinatorially computed from the associated moment cone. As an application we compute the cylindrical…

Let $M, N$ be compact Riemannian manifolds. Then, for fixed volume fraction, in the product of a sufficiently small homothetic copy of $M$ with $N$, every isoperimetric region is the product of $M$ with an isoperimetric region in $N$,…

Let $M$ be a closed, 3-connected, 8-dimensional smooth manifold. In this paper, we compute the concordance inertia group of the product manifold $M\times\mathbb{S}^k$ for $1\leq k\leq 14$ and classify all smooth manifolds homeomorphic to…

A simple convex polytope $P$ is \emph{cohomologically rigid} if its combinatorial structure is determined by the cohomology ring of a quasitoric manifold over $P$. Not every $P$ has this property, but some important polytopes such as…

Two constructions of contact manifolds are presented: (i) products of S^1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic circles. Baykur has found a…

Hybrid computational schemes combining the advantages of a method of moments formulation of a field integral equation and T-matrix method are developed in this paper. The hybrid methods are particularly efficient when describing the…

For a field $\mathbb{F}$ and a triangulated compact $\mathbb{F}$-orientable manifold, consider the homology of the associated Moment-Angle ccomplex $H_*(\mathcal{Z}_{\mathcal{K}})$. We show the total homology rank…

A hex sphere is a singular Euclidean sphere with four cone points whose cone angles are (integer) multiples of $\frac{2\pi}{3}$ but less than $2\pi$. We prove that the Moduli space of hex spheres of unit area is homeomorphic to the the…

An explicit isomorphism between Morse homology and singular homology is constructed via the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a Morse function, the unstable manifolds for the negative…

This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions.…

We construct a weighted version of polyhedral products and compute its cohomology in special cases. This is applied to resolve Steenrod's cohomology realization problem in a case related to products of spheres.

Let $X$ be a torus manifold with locally standard action of a compact torus $T$ of half the dimension and orbit space a homology polytope. Smooth complete complex toric varieties and quasi-toric manifolds are examples of torus manifolds.…

Let $X(P,\lambda)$ be a 4-dimensional toric orbifold associated to a polygon $P$ and a characteristic function $\lambda$. Assuming that $X(P,\lambda)$ is locally smooth over a vertex of $P$, we determine the integral cohomology ring…

Tangent categories provide an axiomatic framework for understanding various tangent bundles and differential operations that occur in differential geometry, algebraic geometry, abstract homotopy theory, and computer science. Previous work…

We identify the cohomology of the stable classifying space of homotopy automorphisms (relative to an embedded disk) of connected sums of $S^k \times S^l$, where $3 \le k < l \le 2k - 2$. The result is expressed in terms of Lie graph complex…

We classify contact manifolds $(M,\mathcal D)$ which are homogeneous under a connected semisimple Lie group $G$, and symmetric in the sense that there exists a contactomorphism of $(M,\mathcal D)$ normalizing $G$, fixing a point $o$ in $M$…

We describe the cohomology of the quotient Z_K/H of a moment-angle complex Z_K by a freely acting subtorus H in T^m by establishing a ring isomorphism of H*(Z_K/H,R) with an appropriate Tor-algebra of the face ring R[K], with coefficients…

Toric topology emerged in the end of the 1990s on the borders of equivariant topology, algebraic and symplectic geometry, combinatorics and commutative algebra. It has quickly grown up into a very active area with many interdisciplinary…

Let $M$ be a smooth, orientable, closed, connected $4$-manifold and suppose that $H_1(M;\mathbb{Z})$ is finitely generated and has no $2$-torsion. We give a homotopy decomposition of the suspension of $M$ in terms of spheres, Moore spaces…