HOMOLOGY TRIVIALITY OF A MAP FROM BRAID GROUP TO MAPPING CLASS GROUP

Title
HOMOLOGY TRIVIALITY OF A MAP FROM BRAID GROUP TO MAPPING CLASS GROUP
Authors
이덕주
Keywords
homologytrivialityofamapfrombraidgrouptomappingclassgroup
Issue Date
2012
Publisher
인하대학교
Abstract
Inside mapping class groups there are rich braid structures which form one of most important characteristics of mapping class groups. We construct a new natural Harer map from braid group to mapping class group, and show that the homology homomorphism induced by this map is a zero map in the stable range for almost all coecients. In the proof of this result, the fact that Harer map factors through the symmetry group plays a key role.
Description
1 Introduction 1 2 Preliminaries 4 2.1 Simplicial Objects and Classifying Spaces 4 2.2 Quillen's Plus-construction 11 2.3 Braid Groups 15 2.4 Mapping Class Groups 21 2.4.1 Dehn Twists 22 3 Homology Triviality of a Harer Map 25 3.1 Splitting Theorem 29 3.2 Construction of a Harer Map 33 3.3 Main Theorem . 35 Bibliography 39
URI
http://dspace.inha.ac.kr/handle/10505/23442
Appears in Collections:
College of Natural Science(자연과학대학) > Mathematics (수학) > Theses(수학 석박사 학위논문)
Files in This Item:
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