Proceedings of the International Geometry Center最新文献_第4页

Proceedings of the International Geometry Center Pub Date : 2022-06-18 DOI: 10.15673/tmgc.v15i1.2139

Тетяна Осіпчук

引用次数: 0

On symplectic invariants of planar 3-webs 平面3-腹板的辛不变量

Proceedings of the International Geometry Center Pub Date : 2022-06-18 DOI: 10.15673/tmgc.v15i1.2058

N. Konovenko

引用次数: 0

Properties of 2-CNF mutually dual and self-dual T_0 -topologies on a finite set and calculation of T_0-topologies of a certain weight 有限集上2-CNF互对偶和自对偶T_0-拓扑的性质及一定权值T_0-拓扑的计算

Proceedings of the International Geometry Center Pub Date : 2022-06-18 DOI: 10.15673/tmgc.v15i1.2084

A. Skryabina, P. Stegantseva, N. Bashova

{"title":"Properties of 2-CNF mutually dual and self-dual T_0 -topologies on a finite set and calculation of T_0-topologies of a certain weight","authors":"A. Skryabina, P. Stegantseva, N. Bashova","doi":"10.15673/tmgc.v15i1.2084","DOIUrl":"https://doi.org/10.15673/tmgc.v15i1.2084","url":null,"abstract":"The problem of counting non-homeomorphic topologies as well as all topologies on an n-elements set is still open. The topologies with the weight k>2n-1, where k is the number of the elements of the topology on an n-elements set, which are called close to the discrete topology have been studied completely. Moreover R.~Stanley in 1971, M.~Kolli in 2007 and in 2014 have been found the number of T0-topologies on an n-elements set with weights k≥7·2n-4, k ≥3·2n-3, and k≥5·2n-4 respectively. \u0000In the present paper we investigate T0-topologies using the topology vector, being an ordered set of the nonnegative integers that define the minimal neighborhoods of the elements of the given finite set, and also using the special form of 2-CNF of Boolean function. In 2021 the authors found the form of the vector of T0-topologies with k≥5·2n-4 and the values k∈[5·2n-4, 2n-1], for which there are no T0-topologies with the weight k. The method of describing of T0-topologies using the special form of 2-CNF of Boolean function is used for the identification of the mutually dual and self-dual T0-topologies, and the properties of such 2-CNF Boolean function are used for counting T0-topologies with the weight 25·2n-6.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75157062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Flows with minimal number of singularities in the Boy's surface 在男孩表面上具有最小奇异数的流

Proceedings of the International Geometry Center Pub Date : 2022-05-23 DOI: 10.15673/tmgc.v15i1.2225

Luca Di Beo, A. Prishlyak

引用次数: 9

A dynamical approach to shape 形状的动态方法

Proceedings of the International Geometry Center Pub Date : 2022-05-21 DOI: 10.15673/tmgc.v15i1.1860

M. Shoptrajanov

引用次数: 0

Relative Gottlieb groups of mapping spaces and their rational cohomology 映射空间的相对Gottlieb群及其有理上同调

Proceedings of the International Geometry Center Pub Date : 2022-05-10 DOI: 10.15673/tmgc.v15i1.2196

A. Zaim

引用次数: 0

Yuriy Yuriyovych Trokhymchuk

Proceedings of the International Geometry Center Pub Date : 2022-02-07 DOI: 10.15673/pigc.v14i3.2205

Y. Drozd, N. Konovenko, S. Maksymenko, S. Plaksa, Olexander Prishlyak

引用次数: 0

Centralizers of elements in Lie algebras of vector fields with polynomial coefficients 多项式系数向量场李代数中元素的中心化器

Proceedings of the International Geometry Center Pub Date : 2022-02-06 DOI: 10.15673/tmgc.v14i4.2153

Анатолій Петрович Петравчук

{"title":"Centralizers of elements in Lie algebras of vector fields with polynomial coefficients","authors":"Анатолій Петрович Петравчук","doi":"10.15673/tmgc.v14i4.2153","DOIUrl":"https://doi.org/10.15673/tmgc.v14i4.2153","url":null,"abstract":"abstract{ukrainian}{Нехай $mathbb K$ -- алгебраїчно замкнене поле харатеристики нуль,$A = mathbb K[x_1,dots,x_n]$ -- кільце многочленів і$R = mathbb K(x_1,dots,x_n)$ -- поле раціональних функцій від $n$ змінних. Позначимо через $W_n = W_n(mathbb K)$ алгебру Лі всіх$mathbb K$-диференціювань на $A$(у випадку $mathbb C$ це алгебра Лі всіх векторних полів на $ mathbb C^n$ з поліноміальними коефіцієнтами). Для заданого $D in W_n(mathbb K)$ будова централізатора$C_{W_n (mathbb K)}(D)$ залежить від поля констант$Ker D = {phi in R | D(phi)=0}$(тут ми природнім чином розширюємо кожне диференціювання $D$ на $A$ на поле $R$).Досліджено випадок, коли $tr.deg_{mathbb K} Ker D le 1$, охарактеризована будова підалгебри $C_{W_n(mathbb K)}(D)$, зокрема доведено, що якщо $Ker D$ не містить несталих многочленів, то$C_{W_n(mathbb K)}(D)$ скінченновимірний над $mathbb K$. Отримано деякі результати про централізатори лінійних диференціювань в $W_n(mathbb K).$}","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77934330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Homeotopy groups of leaf spaces of one-dimensional foliations on non-compact surfaces with non-compact leaves 具有非紧致叶的非紧致表面上一维叶空间的同位群

Proceedings of the International Geometry Center Pub Date : 2022-02-06 DOI: 10.15673/tmgc.v14i4.2204

S. Maksymenko, Eugene Polulyakh Institute of Mathematics of Nas of Ukraine, Kyiv, Ukraine

{"title":"Homeotopy groups of leaf spaces of one-dimensional foliations on non-compact surfaces with non-compact leaves","authors":"S. Maksymenko, Eugene Polulyakh Institute of Mathematics of Nas of Ukraine, Kyiv, Ukraine","doi":"10.15673/tmgc.v14i4.2204","DOIUrl":"https://doi.org/10.15673/tmgc.v14i4.2204","url":null,"abstract":"Let Z be a non-compact two-dimensional manifold obtained from a family of open strips R×(0,1) with boundary intervals by gluing those strips along some pairs of their boundary intervals. Every such strip has a natural foliation into parallel lines R×t, t∊(0,1), and boundary intervals which gives a foliation Δ on all of Z. Denote by H(Z,Δ) the group of all homeomorphisms of Z that maps leaves of Δ onto leaves and by H(Z/Δ) the group of homeomorphisms of the space of leaves endowed with the corresponding compact open topologies. Recently, the authors identified the homeotopy group π0H(Z,Δ) with a group of automorphisms of a certain graph G with additional structure which encodes the combinatorics of gluing Z from strips. That graph is in a certain sense dual to the space of leaves Z/Δ. \u0000On the other hand, for every hinH(Z,Δ) the induced permutation k of leaves of Δ is in fact a homeomorphism of Z/Δ and the correspondence h→k is a homomorphism ψ:H(Δ)→H(Z/Δ). The aim of the present paper is to show that ψ induces a homomorphism of the corresponding homeotopy groups ψ0:π0H(Z,Δ)→π0H(Z/Δ) which turns out to be either injective or having a kernel Z2. This gives a dual description of π0H(Z,Δ) in terms of the space of leaves.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76465985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation (1+3)维齐次monge - ampantere方程的对称约简及若干类不变解

Proceedings of the International Geometry Center Pub Date : 2021-12-24 DOI: 10.15673/tmgc.v14i3.2078

V. Fedorchuk, V. Fedorchuk

引用次数: 0