Constraining mapping class group homomorphisms using finite subgroups
We classify homomorphisms from mapping class groups by using arguments involving finite subgroups. First, we give a new proof of a result of Aramayona–Souto that all homomorphisms between certain mapping class groups of closed surfaces are trivial. Second, we show that only finitely many mapping cla...
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| Veröffentlicht in: | Geometriae dedicata 2024-10, Vol.218 (5), Article 100 |
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| creator | Chen, Lei Lanier, Justin |
| description | We classify homomorphisms from mapping class groups by using arguments involving finite subgroups. First, we give a new proof of a result of Aramayona–Souto that all homomorphisms between certain mapping class groups of closed surfaces are trivial. Second, we show that only finitely many mapping class groups of closed surfaces have nontrivial homomorphisms to
Homeo
(
S
n
)
for any
n
, where
S
n
is the
n
-sphere. We also effectivize this result for small values of
n
; for instance, we prove that every homomorphism from
Mod
(
S
g
)
to
Homeo
(
S
2
)
or
Homeo
(
S
3
)
is trivial if
g
≥
3
, extending a result of Franks–Handel. |
| doi_str_mv | 10.1007/s10711-024-00918-y |
| format | Article |
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Homeo
(
S
n
)
for any
n
, where
S
n
is the
n
-sphere. We also effectivize this result for small values of
n
; for instance, we prove that every homomorphism from
Mod
(
S
g
)
to
Homeo
(
S
2
)
or
Homeo
(
S
3
)
is trivial if
g
≥
3
, extending a result of Franks–Handel.</description><identifier>ISSN: 0046-5755</identifier><identifier>EISSN: 1572-9168</identifier><identifier>DOI: 10.1007/s10711-024-00918-y</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebraic Geometry ; Convex and Discrete Geometry ; Differential Geometry ; Homomorphisms ; Hyperbolic Geometry ; Mapping ; Mathematics ; Mathematics and Statistics ; Original Paper ; Projective Geometry ; Subgroups ; Topology</subject><ispartof>Geometriae dedicata, 2024-10, Vol.218 (5), Article 100</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c244t-4ec5a72fb07878e75579f077c80cac54f3f63bf489d260109460b010f58818783</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10711-024-00918-y$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10711-024-00918-y$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Chen, Lei</creatorcontrib><creatorcontrib>Lanier, Justin</creatorcontrib><title>Constraining mapping class group homomorphisms using finite subgroups</title><title>Geometriae dedicata</title><addtitle>Geom Dedicata</addtitle><description>We classify homomorphisms from mapping class groups by using arguments involving finite subgroups. First, we give a new proof of a result of Aramayona–Souto that all homomorphisms between certain mapping class groups of closed surfaces are trivial. Second, we show that only finitely many mapping class groups of closed surfaces have nontrivial homomorphisms to
Homeo
(
S
n
)
for any
n
, where
S
n
is the
n
-sphere. We also effectivize this result for small values of
n
; for instance, we prove that every homomorphism from
Mod
(
S
g
)
to
Homeo
(
S
2
)
or
Homeo
(
S
3
)
is trivial if
g
≥
3
, extending a result of Franks–Handel.</description><subject>Algebraic Geometry</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Homomorphisms</subject><subject>Hyperbolic Geometry</subject><subject>Mapping</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Projective Geometry</subject><subject>Subgroups</subject><subject>Topology</subject><issn>0046-5755</issn><issn>1572-9168</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kM1KAzEURoMoWKsv4GrAdfQmk0wySynVCgU3ug6ZmEyndH7MnVn07U07gjtJ4FvkfPeGQ8g9g0cGoJ6QgWKMAhcUoGSaHi_IgknFackKfUkWAKKgUkl5TW4Q95AopfiCrFd9h2O0Tdd0ddbaYTilO1jErI79NGS7vk0nDrsGW8wmPL2HhI8-w6k6M3hLroI9oL_7zSX5fFl_rDZ0-_76tnreUseFGKnwTlrFQwVKK-3Tb1QZQCmnwVknRchDkVdB6PKLF8CgFAVUKYPUmqVGviQP89wh9t-Tx9Hs-yl2aaXJkwFRpJsnis-Uiz1i9MEMsWltPBoG5qTLzLpM0mXOuswxlfK5hAnuah__Rv_T-gF65G3G</recordid><startdate>20241001</startdate><enddate>20241001</enddate><creator>Chen, Lei</creator><creator>Lanier, Justin</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20241001</creationdate><title>Constraining mapping class group homomorphisms using finite subgroups</title><author>Chen, Lei ; Lanier, Justin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c244t-4ec5a72fb07878e75579f077c80cac54f3f63bf489d260109460b010f58818783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algebraic Geometry</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Homomorphisms</topic><topic>Hyperbolic Geometry</topic><topic>Mapping</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Projective Geometry</topic><topic>Subgroups</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Lei</creatorcontrib><creatorcontrib>Lanier, Justin</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Lei</au><au>Lanier, Justin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Constraining mapping class group homomorphisms using finite subgroups</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2024-10-01</date><risdate>2024</risdate><volume>218</volume><issue>5</issue><artnum>100</artnum><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>We classify homomorphisms from mapping class groups by using arguments involving finite subgroups. First, we give a new proof of a result of Aramayona–Souto that all homomorphisms between certain mapping class groups of closed surfaces are trivial. Second, we show that only finitely many mapping class groups of closed surfaces have nontrivial homomorphisms to
Homeo
(
S
n
)
for any
n
, where
S
n
is the
n
-sphere. We also effectivize this result for small values of
n
; for instance, we prove that every homomorphism from
Mod
(
S
g
)
to
Homeo
(
S
2
)
or
Homeo
(
S
3
)
is trivial if
g
≥
3
, extending a result of Franks–Handel.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-024-00918-y</doi><oa>free_for_read</oa></addata></record> |
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| ispartof | Geometriae dedicata, 2024-10, Vol.218 (5), Article 100 |
| issn | 0046-5755 1572-9168 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algebraic Geometry Convex and Discrete Geometry Differential Geometry Homomorphisms Hyperbolic Geometry Mapping Mathematics Mathematics and Statistics Original Paper Projective Geometry Subgroups Topology |
| title | Constraining mapping class group homomorphisms using finite subgroups |
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