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Linear representations of Aut(Fr) on the homology of representation varieties
Let G be a compact semisimple linear Lie group. We study the action of Aut ( F r ) on the space H ∗ ( G r ; Q ) . We compute the image of this representation and prove that it only depends on the rank of g . We show that the kernel of this representation is always the Torrelli subgroup IA r of Aut (...
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| Published in: | Geometriae dedicata 2020-12, Vol.209 (1), p.199-206 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-p227t-5147413f228225d9cf9ec947a92aa6d0659641a9442ee5c1e3e205b167b9e1383 |
| container_end_page | 206 |
| container_issue | 1 |
| container_start_page | 199 |
| container_title | Geometriae dedicata |
| container_volume | 209 |
| creator | Algom-Kfir, Yael Hadari, Asaf |
| description | Let
G
be a compact semisimple linear Lie group. We study the action of
Aut
(
F
r
)
on the space
H
∗
(
G
r
;
Q
)
. We compute the image of this representation and prove that it only depends on the rank of
g
. We show that the kernel of this representation is always the Torrelli subgroup
IA
r
of
Aut
(
F
r
)
. |
| doi_str_mv | 10.1007/s10711-020-00530-w |
| format | article |
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G
be a compact semisimple linear Lie group. We study the action of
Aut
(
F
r
)
on the space
H
∗
(
G
r
;
Q
)
. We compute the image of this representation and prove that it only depends on the rank of
g
. We show that the kernel of this representation is always the Torrelli subgroup
IA
r
of
Aut
(
F
r
)
.</description><identifier>ISSN: 0046-5755</identifier><identifier>EISSN: 1572-9168</identifier><identifier>DOI: 10.1007/s10711-020-00530-w</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Algebraic Geometry ; Convex and Discrete Geometry ; Differential Geometry ; Homology ; Hyperbolic Geometry ; Lie groups ; Mathematics ; Mathematics and Statistics ; Original Paper ; Projective Geometry ; Representations ; Subgroups ; Topology</subject><ispartof>Geometriae dedicata, 2020-12, Vol.209 (1), p.199-206</ispartof><rights>Springer Nature B.V. 2020</rights><rights>Springer Nature B.V. 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p227t-5147413f228225d9cf9ec947a92aa6d0659641a9442ee5c1e3e205b167b9e1383</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Algom-Kfir, Yael</creatorcontrib><creatorcontrib>Hadari, Asaf</creatorcontrib><title>Linear representations of Aut(Fr) on the homology of representation varieties</title><title>Geometriae dedicata</title><addtitle>Geom Dedicata</addtitle><description>Let
G
be a compact semisimple linear Lie group. We study the action of
Aut
(
F
r
)
on the space
H
∗
(
G
r
;
Q
)
. We compute the image of this representation and prove that it only depends on the rank of
g
. We show that the kernel of this representation is always the Torrelli subgroup
IA
r
of
Aut
(
F
r
)
.</description><subject>Algebraic Geometry</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Homology</subject><subject>Hyperbolic Geometry</subject><subject>Lie groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Projective Geometry</subject><subject>Representations</subject><subject>Subgroups</subject><subject>Topology</subject><issn>0046-5755</issn><issn>1572-9168</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpVkE1LAzEURYMoWKt_wNWAG11E38tnsyzFqlBxo-uQtm_aKXUyJqnFf29rBXF1F_dwLxzGLhFuEcDeZQSLyEEAB9AS-PaI9VBbwR2awTHrASjDtdX6lJ3lvAIAZ63osedJ01JIVaIuUaa2hNLENlexroabcj1ON1Vsq7Kkahnf4zouvvbVf7r6DKmh0lA-Zyd1WGe6-M0-exvfv44e-eTl4Wk0nPBOCFu4RmUVylqIgRB67ma1o5lTNjgRgpmD0c4oDE4pQaRnSJIE6CkaO3WEciD77Oqw26X4saFc_CpuUru79EJp1MqgsztKHqjcpaZdUPqjEPzemz948ztv_seb38pvxPpgEA</recordid><startdate>20201201</startdate><enddate>20201201</enddate><creator>Algom-Kfir, Yael</creator><creator>Hadari, Asaf</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>20201201</creationdate><title>Linear representations of Aut(Fr) on the homology of representation varieties</title><author>Algom-Kfir, Yael ; Hadari, Asaf</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p227t-5147413f228225d9cf9ec947a92aa6d0659641a9442ee5c1e3e205b167b9e1383</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Algebraic Geometry</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Homology</topic><topic>Hyperbolic Geometry</topic><topic>Lie groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Projective Geometry</topic><topic>Representations</topic><topic>Subgroups</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Algom-Kfir, Yael</creatorcontrib><creatorcontrib>Hadari, Asaf</creatorcontrib><jtitle>Geometriae dedicata</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Algom-Kfir, Yael</au><au>Hadari, Asaf</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Linear representations of Aut(Fr) on the homology of representation varieties</atitle><jtitle>Geometriae dedicata</jtitle><stitle>Geom Dedicata</stitle><date>2020-12-01</date><risdate>2020</risdate><volume>209</volume><issue>1</issue><spage>199</spage><epage>206</epage><pages>199-206</pages><issn>0046-5755</issn><eissn>1572-9168</eissn><abstract>Let
G
be a compact semisimple linear Lie group. We study the action of
Aut
(
F
r
)
on the space
H
∗
(
G
r
;
Q
)
. We compute the image of this representation and prove that it only depends on the rank of
g
. We show that the kernel of this representation is always the Torrelli subgroup
IA
r
of
Aut
(
F
r
)
.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10711-020-00530-w</doi><tpages>8</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0046-5755 |
| ispartof | Geometriae dedicata, 2020-12, Vol.209 (1), p.199-206 |
| issn | 0046-5755 1572-9168 |
| language | eng |
| recordid | cdi_proquest_journals_2451546197 |
| source | Springer Link |
| subjects | Algebraic Geometry Convex and Discrete Geometry Differential Geometry Homology Hyperbolic Geometry Lie groups Mathematics Mathematics and Statistics Original Paper Projective Geometry Representations Subgroups Topology |
| title | Linear representations of Aut(Fr) on the homology of representation varieties |
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