{"title":"内爆、收缩和摩尔-立川","authors":"Andrew Dancer, Frances Kirwan, Johan Martens","doi":"10.1142/s0129167x24410040","DOIUrl":null,"url":null,"abstract":"<p>We give a survey of the implosion construction, extending some of its aspects relating to hypertoric geometry from type <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>A</mi></math></span><span></span> to a general reductive group, and interpret it in the context of the Moore–Tachikawa category. We use these ideas to discuss how the contraction construction in symplectic geometry can be generalized to the hyperkähler or complex symplectic situation.</p>","PeriodicalId":54951,"journal":{"name":"International Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Implosion, contraction and Moore–Tachikawa\",\"authors\":\"Andrew Dancer, Frances Kirwan, Johan Martens\",\"doi\":\"10.1142/s0129167x24410040\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We give a survey of the implosion construction, extending some of its aspects relating to hypertoric geometry from type <span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>A</mi></math></span><span></span> to a general reductive group, and interpret it in the context of the Moore–Tachikawa category. We use these ideas to discuss how the contraction construction in symplectic geometry can be generalized to the hyperkähler or complex symplectic situation.</p>\",\"PeriodicalId\":54951,\"journal\":{\"name\":\"International Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-03-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0129167x24410040\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0129167x24410040","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们考察了内爆构造，将其与高折射几何有关的某些方面从 A 型扩展到一般还原群，并在摩尔-立川范畴的背景下对其进行了解释。我们利用这些观点来讨论如何将交点几何中的内卷构造推广到超交点或复交点情形中。
We give a survey of the implosion construction, extending some of its aspects relating to hypertoric geometry from type to a general reductive group, and interpret it in the context of the Moore–Tachikawa category. We use these ideas to discuss how the contraction construction in symplectic geometry can be generalized to the hyperkähler or complex symplectic situation.
期刊介绍：
The International Journal of Mathematics publishes original papers in mathematics in general, but giving a preference to those in the areas of mathematics represented by the editorial board. The journal has been published monthly except in June and December to bring out new results without delay. Occasionally, expository papers of exceptional value may also be published. The first issue appeared in March 1990.
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