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International Journal of Mathematics
Article . 2013 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2012
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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THE PILLAR SWITCHINGS OF MAPPING CLASS GROUPS OF SURFACES

Authors: Chan-Seok Jeong; Yongjin Song;

THE PILLAR SWITCHINGS OF MAPPING CLASS GROUPS OF SURFACES

Abstract

By gluing two copies of surface S0,g+2 along g + 1 holes, we get surface Sg,1. The pillar switching is a self-homeomorphism of Sg,1 which switches two pillars of surfaces by 180° horizontal rotation. We analyze the actions of the pillar switchings on π1Sg,1 and then give concrete expressions of the pillar switchings in terms of standard Dehn twists. The map ψ : Bg → Γg,1 sending the generators of Bg to the pillar switchings on Sg,1 is defined by extending the embedding Bg ↪ Γ0,(g+1),1. We show that this map is injective by analyzing the actions of pillar switchings on π1Sg,1. We also prove that this map induces a trivial homology homomorphism in the stable range. For the proof we use the categorical delooping method. We construct a suitable monoidal 2-functor from tile category to surface category and show that this functor thus induces a map of double loop spaces.

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Keywords

55P48, 55R37, 57M50, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Green
bronze
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