Separating subgroups of mapping class groups in homological representations
Keyword(s):
Let [Formula: see text] be either the mapping class group of a closed surface of genus [Formula: see text], or the automorphism group of a free group of rank [Formula: see text]. Given any homological representation [Formula: see text] of [Formula: see text] corresponding to a finite cover, and any term [Formula: see text] of the Johnson filtration, we show that [Formula: see text] has finite index in [Formula: see text], the Torelli subgroup of [Formula: see text]. Since [Formula: see text] for [Formula: see text], this implies for instance that no such representation is faithful.
2001 ◽
Vol 10
(05)
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pp. 763-767
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2017 ◽
Vol 26
(07)
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pp. 1750037
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2015 ◽
Vol 24
(07)
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pp. 1550034
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2010 ◽
Vol 20
(03)
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pp. 437-456
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1998 ◽
Vol 123
(3)
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pp. 487-499
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