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PSP volume 173 issue 1 Cover and Front matter PSP第173卷第1期封面和封面问题
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-06-13 DOI: 10.1017/s0305004122000275
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引用次数: 0
PSP volume 173 issue 1 Cover and Back matter PSP第173卷第1期封面和封底
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-06-13 DOI: 10.1017/s0305004122000287
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引用次数: 0
Intersection theorems for finite general linear groups 有限一般线性群的交点定理
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-05-17 DOI: 10.1017/S0305004123000075
Alena Ernst, K. Schmidt
{"title":"Intersection theorems for finite general linear groups","authors":"Alena Ernst, K. Schmidt","doi":"10.1017/S0305004123000075","DOIUrl":"https://doi.org/10.1017/S0305004123000075","url":null,"abstract":"Abstract A subset Y of the general linear group \u0000$text{GL}(n,q)$\u0000 is called t-intersecting if \u0000$text{rk}(x-y)le n-t$\u0000 for all \u0000$x,yin Y$\u0000 , or equivalently x and y agree pointwise on a t-dimensional subspace of \u0000$mathbb{F}_q^n$\u0000 for all \u0000$x,yin Y$\u0000 . We show that, if n is sufficiently large compared to t, the size of every such t-intersecting set is at most that of the stabiliser of a basis of a t-dimensional subspace of \u0000$mathbb{F}_q^n$\u0000 . In case of equality, the characteristic vector of Y is a linear combination of the characteristic vectors of the cosets of these stabilisers. We also give similar results for subsets of \u0000$text{GL}(n,q)$\u0000 that intersect not necessarily pointwise in t-dimensional subspaces of \u0000$mathbb{F}_q^n$\u0000 and for cross-intersecting subsets of \u0000$text{GL}(n,q)$\u0000 . These results may be viewed as variants of the classical Erdős–Ko–Rado Theorem in extremal set theory and are q-analogs of corresponding results known for the symmetric group. Our methods are based on eigenvalue techniques to estimate the size of the largest independent sets in graphs and crucially involve the representation theory of \u0000$text{GL}(n,q)$\u0000 .","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"81 1","pages":"129 - 160"},"PeriodicalIF":0.8,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76892137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
PSP volume 172 issue 3 Cover and Front matter PSP卷172问题3封面和前面的问题
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-05-01 DOI: 10.1017/s0305004122000184
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引用次数: 0
PSP volume 172 issue 3 Cover and Back matter PSP第172卷第3期封面和封底
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-05-01 DOI: 10.1017/s0305004122000196
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引用次数: 0
On the integral Hodge conjecture for varieties with trivial Chow group 具有平凡Chow群的变量的积分Hodge猜想
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-04-28 DOI: 10.1017/S0305004123000233
Humberto A. Diaz
{"title":"On the integral Hodge conjecture for varieties with trivial Chow group","authors":"Humberto A. Diaz","doi":"10.1017/S0305004123000233","DOIUrl":"https://doi.org/10.1017/S0305004123000233","url":null,"abstract":"Abstract We obtain examples of smooth projective varieties over \u0000${mathbb C}$\u0000 that violate the integral Hodge conjecture and for which the total Chow group is of finite rank. Moreover, we show that there exist such examples defined over number fields.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"56 1","pages":"433 - 443"},"PeriodicalIF":0.8,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89378461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On the values taken by slice torus invariants 关于切片环面不变量取的值
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-02-28 DOI: 10.1017/s0305004123000403
P. Feller, Lukas Lewark, A. Lobb
{"title":"On the values taken by slice torus invariants","authors":"P. Feller, Lukas Lewark, A. Lobb","doi":"10.1017/s0305004123000403","DOIUrl":"https://doi.org/10.1017/s0305004123000403","url":null,"abstract":"\u0000 We study the space of slice torus invariants. In particular we characterise the set of values that slice torus invariants may take on a given knot in terms of the stable smooth slice genus. Our study reveals that the resolution of the local Thom conjecture implies the existence of slice torus invariants without having to appeal to any explicit construction from a knot homology theory.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"33 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72529414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
PSP volume 172 issue 2 Cover and Front matter PSP卷172第2期封面和前面的问题
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-02-11 DOI: 10.1017/s0305004122000044
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引用次数: 0
PSP volume 172 issue 2 Cover and Back matter PSP卷172第2期封面和背面
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-02-11 DOI: 10.1017/s0305004122000056
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引用次数: 0
Null-homotopic knots have Property R 零同伦结有性质R
IF 0.8 3区 数学
Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-01-25 DOI: 10.1017/S0305004123000129
Yi Ni
{"title":"Null-homotopic knots have Property R","authors":"Yi Ni","doi":"10.1017/S0305004123000129","DOIUrl":"https://doi.org/10.1017/S0305004123000129","url":null,"abstract":"Abstract We prove that if K is a nontrivial null-homotopic knot in a closed oriented 3–manfiold Y such that \u0000$Y-K$\u0000 does not have an \u0000$S^1times S^2$\u0000 summand, then the zero surgery on K does not have an \u0000$S^1times S^2$\u0000 summand. This generalises a result of Hom and Lidman, who proved the case when Y is an irreducible rational homology sphere.","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"107 1","pages":"217 - 223"},"PeriodicalIF":0.8,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79574808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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