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The product structure on loop homology : 루프 호모로지의 연산구조
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | Otto van Koert | - |
| dc.contributor.author | 조명신 | - |
| dc.date.accessioned | 2018-12-03T01:55:58Z | - |
| dc.date.available | 2018-12-03T01:55:58Z | - |
| dc.date.issued | 2018-08 | - |
| dc.identifier.other | 000000152174 | - |
| dc.identifier.uri | https://hdl.handle.net/10371/144226 | - |
| dc.description | 학위논문 (석사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 8. Otto van Koert. | - |
| dc.description.abstract | In this paper, we survey the result of R. Cohen and J. Jones on the Chas-Sullivan product.
Briefly, Cohen and Jones precisely defined the Chas-Sullivan product using ring spectra, and show that the Chas-Sullivan product coincides with the cup product structure on the Hochschild cohomology of the cochain complex of the base manifold. In the sequel paper, they introduce a loop homology spectral sequence and compute the algebra structure on the free loop space of spheres and complex projective spaces. | - |
| dc.description.tableofcontents | Contents
Abstract i 1 Preliminaries 1 1.1 Intersection product on closed oriented smooth manifolds . . . . . . . . . 1 1.2 Stable homotopy theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Pontrjagin-Thom construction . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Intersection product via ring spectrum . . . . . . . . . . . . . . . . . . . 8 1.5 Hochschild (co)homology and cosimplicial model . . . . . . . . . . . . . 9 2 Chas-Sullivan Product 12 2.1 The original idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Chas-Sullivan product and ring spectra . . . . . . . . . . . . . . . . . . . 13 2.3 Cosimplicial model and Hochschild cohomology . . . . . . . . . . . . . 16 3 Computations and Examples 23 3.1 Loop Homology Spectral Sequence . . . . . . . . . . . . . . . . . . . . 23 3.1.1 Free loop space of spheres . . . . . . . . . . . . . . . . . . . . . 25 3.1.2 Free loop space of complex projective spaces . . . . . . . . . . . 28 References 30 Abstract (in Korean) 32 | - |
| dc.format | application/pdf | - |
| dc.format.medium | application/pdf | - |
| dc.language.iso | ko | - |
| dc.publisher | 서울대학교 대학원 | - |
| dc.subject.ddc | 510 | - |
| dc.title | The product structure on loop homology | - |
| dc.title.alternative | 루프 호모로지의 연산구조 | - |
| dc.type | Thesis | - |
| dc.contributor.AlternativeAuthor | Cho Myungsin | - |
| dc.description.degree | Master | - |
| dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
| dc.date.awarded | 2018-08 | - |
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