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Signature of Surface bundles over Surfaces and Mapping Class Group : 곡면 위의 곡면 다발의 부호수와 사상류 군
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 박종일 | - |
dc.contributor.author | 이주아 | - |
dc.date.accessioned | 2017-07-14T00:43:11Z | - |
dc.date.available | 2017-07-14T00:43:11Z | - |
dc.date.issued | 2017-02 | - |
dc.identifier.other | 000000142027 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121326 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2017. 2. 박종일. | - |
dc.description.abstract | In this thesis, we study the topological constraints on the signature and the
Euler characteristic (σ(X) | - |
dc.description.abstract | e(X)) for smooth 4-manifolds X (or complex surfaces
X) which are surface bundles over surfaces with nonzero signature. The first main result is about the improved upper bounds for the minimal base genus function b(f | - |
dc.description.abstract | n) for a fixed fiber genus f and a fixed signature 4n. In
particular, we construct new smooth 4-manifolds with a fixed signature 4 and small Euler characteristic which are surface bundles over surfaces by subtraction of Lefschetz fibrations. They include an example with the smallest Euler characteristic among known examples with non-zero signature. Secondly, we explore possibilities to construct Kodaira fibrations with small signature which are smooth surface bundles over surfaces as ramified coverings of products of two complex curves. To obtain the minimal base genus and the smallest possible signature, we investigate the action of the monodromy of the fibration of pointed curves. Throughout the paper well see that the surface mapping class group plays an important role in both constructions and the control of topological invariants. | - |
dc.description.tableofcontents | 1 Introduction 1
2 Signature of fibered 4-manifolds 7 2.1 Signature of 4-manifolds 7 2.2 Surface bundles over surfaces and Lefschetz fibrations 9 2.3 Various signature formulas for surface bundles 10 3 Mapping class group 13 3.1 Presentation of Mapping class group 14 3.2 Homology of Mapping class group 15 3.3 Birman exact sequence 17 4 Surface bundles over surfaces with a fixed signature 20 4.1 Preliminaries 21 4.1.1 Signature 21 4.1.2 Mapping class group 21 4.1.3 Lefschetz fibrations and surface bundles 23 4.2 Subtraction of Lefschetz fibrations 24 4.3 Signature computation 35 5 Double Kodaira fibartions with small signature 40 5.1 Kodaira fibrations 40 5.2 Effective tautological construction 43 5.2.1 Construction: if D contains a graph 44 5.2.2 Construction: general case 45 5.3 Method to compute monodromy action 49 5.4 Virtual Kodaira fibrations with small realisation signature 56 5.4.1 Numerical classification of virtual Kodaira fibrations of virtual signature 4 56 5.4.2 Automorphisms without fixed points on curves of small genus 59 5.5 Computing realisation signature: examples 62 5.5.1 Examples of graph type 63 5.5.2 Examples of correspondence type 71 Bibliography 83 Abstract (in Korean) 89 | - |
dc.format | application/pdf | - |
dc.format.extent | 848026 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | signature | - |
dc.subject | surface bundles over surfaces | - |
dc.subject | mapping class group | - |
dc.subject | Lefschetz fibration | - |
dc.subject | Kodaira fibration | - |
dc.subject | Birman exact sequence | - |
dc.subject.ddc | 510 | - |
dc.title | Signature of Surface bundles over Surfaces and Mapping Class Group | - |
dc.title.alternative | 곡면 위의 곡면 다발의 부호수와 사상류 군 | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | Ju A Lee | - |
dc.description.degree | Doctor | - |
dc.citation.pages | 88 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2017-02 | - |
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