{"title":"矩形中正方形的构形空间","authors":"L. Plachta","doi":"10.2140/agt.2021.21.1445","DOIUrl":null,"url":null,"abstract":"The configuration space Fk(Q,r) of k squares of size r in a rectangle Q is studied with the help of the tautological function 𝜃 defined on the affine polytope complex Qk. The critical points of the function 𝜃 are described in geometric and combinatorial terms. We also show that under certain conditions, the space Fk(Q,r) is connected.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"29 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Configuration spaces of squares in a rectangle\",\"authors\":\"L. Plachta\",\"doi\":\"10.2140/agt.2021.21.1445\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The configuration space Fk(Q,r) of k squares of size r in a rectangle Q is studied with the help of the tautological function 𝜃 defined on the affine polytope complex Qk. The critical points of the function 𝜃 are described in geometric and combinatorial terms. We also show that under certain conditions, the space Fk(Q,r) is connected.\",\"PeriodicalId\":50826,\"journal\":{\"name\":\"Algebraic and Geometric Topology\",\"volume\":\"29 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-08-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic and Geometric Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/agt.2021.21.1445\",\"RegionNum\":3,\"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":"Algebraic and Geometric Topology","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/agt.2021.21.1445","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The configuration space Fk(Q,r) of k squares of size r in a rectangle Q is studied with the help of the tautological function 𝜃 defined on the affine polytope complex Qk. The critical points of the function 𝜃 are described in geometric and combinatorial terms. We also show that under certain conditions, the space Fk(Q,r) is connected.
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