Related papers: Moment-angle manifolds and Panov's problem
We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold.…
We introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. The main result of this paper is that the Chekanov-Eliashberg dg-algebra of the attaching spheres of a Weinstein manifold satisfies a…
First, we analyze the discrete Monge--Kantorovich problem, linking it with the minimization problem of linear functionals over adjoint orbits. Second, we consider its generalization to the setting of area preserving diffeomorphisms of the…
Based on recent work on simplicial diffeomorphisms in colored group field theories, we develop a representation of the colored Boulatov model, in which the GFT fields depend on variables associated to vertices of the associated simplicial…
We construct open book structures on all moment-angle manifolds and describe the topology of their leaves and bindings under certain restrictions. II. We also show, using a recent deep result about contact forms due to Borman, Eliashberg…
In this paper, we introduce new generalized barycentric coordinates (coined as {\em moment coordinates}) on nonconvex quadrilaterals and convex hexahedra with planar faces. This work draws on recent advances in constructing interpolants to…
Topological methods have emerged as valuable tools for analyzing the structural properties of directed graphs, particularly connectome data in computational neuroscience. This paper investigates the construction of topological spaces from…
Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in…
In this article, we study the cohomology ring of real moment-angle complexes over a simplicial complex $K$. Combinatorial generators for the cohomology can be given in terms of $K$. For $K$ the boundary of an $n$-gon, we give a full…
One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their…
We study the computation of local approximations of invariant manifolds of parabolic fixed points and parabolic periodic orbits of periodic vector fields. If the dimension of these manifolds is two or greater, in general, it is not possible…
A simplicial complement P is a sequence of subsets of [m] and the simplicial complement P corresponds to a unique simplicial complex K with vertices in [m]. In this paper, we defined the homology of a simplicial complement…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
We construct the symplectic resolution of a symplectic orbifold whose isotropy locus consists of disjoint submanifolds with homogeneous isotropy, that is, all its points have the same isotropy groups.
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold ("phase space"). His algorithm gives a non-commutative, but…
Let $M$ be a closed simply connected $7$-manifold. In this paper we establish homotopy decompositions of the reduced suspension space $\Sigma M$ into a wedge sum of simpler spaces when localized at a set of primes. These decompositions are…
We present an explicit example of a fast decaying solution to the modified Novikov--Veselov equation with a one-point singularity in the space-time. It is constructed by using the geometrical interpretation of the Moutard transformation of…
Following on from ``Hyperbolic Plateau problems'' (by the same author), we provide a complete geometric description of solutions to the Plateau problem $(S,\phi)$ when $S$ is a compact Riemann surface with a finite number of points removed.
The theory of holomorphic functions of several complex variables is applied in proving a multidimensional variant of a theorem involving an exponential boundedness criterion for the classical moment problem. A theorem of Petersen concerning…
It is a well-known result of C.T.C. Wall's that one may decompose a simply connected 6-manifold as a connected sum of two simpler manifolds. Recent work of Beben and Theriault on decomposing based loop spaces of highly connected Poincar\'e…