J. Gatsinzi
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{"title":"复杂格拉斯曼群之间的相对Gottlieb群嵌入","authors":"J. Gatsinzi","doi":"10.1155/2021/1417769","DOIUrl":null,"url":null,"abstract":"<jats:p>Let <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mtext>Gr</mtext>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>k</mi>\n <mo>,</mo>\n <mi>n</mi>\n </mrow>\n </mfenced>\n </math>\n </jats:inline-formula> be the complex Grassmann manifold of <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <mi>k</mi>\n </math>\n </jats:inline-formula>-linear subspaces in <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <msup>\n <mrow>\n <mi>ℂ</mi>\n </mrow>\n <mrow>\n <mi>n</mi>\n </mrow>\n </msup>\n </math>\n </jats:inline-formula>. We compute rational relative Gottlieb groups of the embedding <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\n <mi>i</mi>\n <mo>:</mo>\n <mtext>Gr</mtext>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>k</mi>\n <mo>,</mo>\n <mi>n</mi>\n </mrow>\n </mfenced>\n <mo>⟶</mo>\n <mtext>Gr</mtext>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>k</mi>\n <mo>,</mo>\n <mi>n</mi>\n <mo>+</mo>\n <mi>r</mi>\n </mrow>\n </mfenced>\n </math>\n </jats:inline-formula> and show that the <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\n <mi>G</mi>\n </math>\n </jats:inline-formula>-sequence is exact if <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\n <mi>r</mi>\n <mo>≥</mo>\n <mi>k</mi>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mi>n</mi>\n <mo>−</mo>\n <mi>k</mi>\n </mrow>\n </mfenced>\n </math>\n </jats:inline-formula>.</jats:p>","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2021-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Relative Gottlieb Groups of Embeddings between Complex Grassmannians\",\"authors\":\"J. Gatsinzi\",\"doi\":\"10.1155/2021/1417769\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<jats:p>Let <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <mtext>Gr</mtext>\\n <mfenced open=\\\"(\\\" close=\\\")\\\" separators=\\\"|\\\">\\n <mrow>\\n <mi>k</mi>\\n <mo>,</mo>\\n <mi>n</mi>\\n </mrow>\\n </mfenced>\\n </math>\\n </jats:inline-formula> be the complex Grassmann manifold of <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <mi>k</mi>\\n </math>\\n </jats:inline-formula>-linear subspaces in <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M3\\\">\\n <msup>\\n <mrow>\\n <mi>ℂ</mi>\\n </mrow>\\n <mrow>\\n <mi>n</mi>\\n </mrow>\\n </msup>\\n </math>\\n </jats:inline-formula>. We compute rational relative Gottlieb groups of the embedding <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M4\\\">\\n <mi>i</mi>\\n <mo>:</mo>\\n <mtext>Gr</mtext>\\n <mfenced open=\\\"(\\\" close=\\\")\\\" separators=\\\"|\\\">\\n <mrow>\\n <mi>k</mi>\\n <mo>,</mo>\\n <mi>n</mi>\\n </mrow>\\n </mfenced>\\n <mo>⟶</mo>\\n <mtext>Gr</mtext>\\n <mfenced open=\\\"(\\\" close=\\\")\\\" separators=\\\"|\\\">\\n <mrow>\\n <mi>k</mi>\\n <mo>,</mo>\\n <mi>n</mi>\\n <mo>+</mo>\\n <mi>r</mi>\\n </mrow>\\n </mfenced>\\n </math>\\n </jats:inline-formula> and show that the <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M5\\\">\\n <mi>G</mi>\\n </math>\\n </jats:inline-formula>-sequence is exact if <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M6\\\">\\n <mi>r</mi>\\n <mo>≥</mo>\\n <mi>k</mi>\\n <mfenced open=\\\"(\\\" close=\\\")\\\" separators=\\\"|\\\">\\n <mrow>\\n <mi>n</mi>\\n <mo>−</mo>\\n <mi>k</mi>\\n </mrow>\\n </mfenced>\\n </math>\\n </jats:inline-formula>.</jats:p>\",\"PeriodicalId\":39893,\"journal\":{\"name\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2021-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2021/1417769\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2021/1417769","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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