THE BRAIDINGS IN THE MAPPING CLASS GROUPS OF SURFACES

Title
THE BRAIDINGS IN THE MAPPING CLASS GROUPS OF SURFACES
Authors
송용진
Issue Date
2013
Publisher
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
Series/Report no.
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY ; Vol50 no.4 Startpage 865 Endpage 877
Abstract
The disjoint union of mapping class groups of surfaces forms a braided monoidal category M, as the disjoint union of the braid groups B does. We give a concrete and geometric meaning of the braidings βr,s in M. Moreover, we find a set of elements in the mapping class groups which correspond to the standard generators of the braid groups. Using this, we can define an obvious map φ : Bg → Γg,1. We show that this map φ is injective and nongeometric in the sense of Wajnryb. Since this map extends to a braided monoidal functor Φ : B → M, the integral homology homomorphism induced by φ is trivial in the stable range
URI
http://dx.doi.org/10.4134/JKMS.2013.50.4.865
http://dspace.inha.ac.kr/handle/10505/33370
ISSN
0304-9914
Appears in Collections:
College of Natural Science(자연과학대학) > Mathematics (수학) > Local Access Journal Papers, Reports(수학 논문, 보고서)

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