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The compatibility of the filtration of mapping class groups of two surfaces pasted along the boundaries

✍ Scribed by Mamoru Asada

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
139 KB
Volume
108
Category
Article
ISSN
0166-8641

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✦ Synopsis

Let Ξ£ n g be an orientable surface of genus g 0 with n 0 punctures and Ξ“ n g be its pure mapping class group. The group Ξ“ n g has a filtration {Ξ“ n g [m]} m 1 induced from its action on the fundamental group of Ann. 304 (1996) 99], which is induced from pasting two surfaces with one boundary component along their boundaries. That this homomorphism preserves the filtration strictly has been shown by Nakamura in the case that n 1. We shall show that this holds also in the case that n = 0.

As an application, we obtain a lower bound of the rank of the graded module associated with the filtration of Ξ“ g (= Ξ“ 0 g ).

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