{"title":"重力谱序列e1项的研究","authors":"D. Tamaki","doi":"10.2140/gtm.2007.10.347","DOIUrl":null,"url":null,"abstract":"The author constructed a spectral sequence strongly converging to h_*(Omega^n Sigma^n X) for any homology theory in [Topology 33 (1994) 631-662]. In this note, we prove that the E^1-term of the spectral sequence is isomorphic to the cobar construction, and hence the spectral sequence is isomorphic to the classical cobar-type Eilenberg-Moore spectral sequence based on the geometric cobar construction from the E^1-term. Similar arguments can be also applied to its variants constructed in [Contemp Math 293 (2002) 299-329].","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"213 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On the E 1 -term of the gravity spectral sequence\",\"authors\":\"D. Tamaki\",\"doi\":\"10.2140/gtm.2007.10.347\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The author constructed a spectral sequence strongly converging to h_*(Omega^n Sigma^n X) for any homology theory in [Topology 33 (1994) 631-662]. In this note, we prove that the E^1-term of the spectral sequence is isomorphic to the cobar construction, and hence the spectral sequence is isomorphic to the classical cobar-type Eilenberg-Moore spectral sequence based on the geometric cobar construction from the E^1-term. Similar arguments can be also applied to its variants constructed in [Contemp Math 293 (2002) 299-329].\",\"PeriodicalId\":115248,\"journal\":{\"name\":\"Geometry and Topology Monographs\",\"volume\":\"213 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry and Topology Monographs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/gtm.2007.10.347\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry and Topology Monographs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gtm.2007.10.347","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The author constructed a spectral sequence strongly converging to h_*(Omega^n Sigma^n X) for any homology theory in [Topology 33 (1994) 631-662]. In this note, we prove that the E^1-term of the spectral sequence is isomorphic to the cobar construction, and hence the spectral sequence is isomorphic to the classical cobar-type Eilenberg-Moore spectral sequence based on the geometric cobar construction from the E^1-term. Similar arguments can be also applied to its variants constructed in [Contemp Math 293 (2002) 299-329].
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