Homology of the family of hyperelliptic curves
Homology of braid groups and Artin groups can be related to the study of spaces of curves. We completely calculate the integral homology of the family of smooth curves of genus g with one boundary component, that are double coverings of the disk ramified over n = 2 g +1 points. The main part of such...
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| Veröffentlicht in: | Israel journal of mathematics 2019-03, Vol.230 (2), p.653-692 |
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| container_title | Israel journal of mathematics |
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| creator | Callegaro, Filippo Salvetti, Mario |
| description | Homology of braid groups and Artin groups can be related to the study of spaces of curves. We completely calculate the integral homology of the family of smooth curves of genus
g
with one boundary component, that are double coverings of the disk ramified over
n
= 2
g
+1 points. The main part of such homology is described by the homology of the braid group with coefficients in a symplectic representation, namely the braid group Br
n
acts on the first homology group of a genus
g
surface via Dehn twists. Our computations show that such groups have only 2-torsion. We also investigate stabilization properties and provide Poincaré series, for both unstable and stable homology. |
| doi_str_mv | 10.1007/s11856-019-1832-3 |
| format | Article |
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g
with one boundary component, that are double coverings of the disk ramified over
n
= 2
g
+1 points. The main part of such homology is described by the homology of the braid group with coefficients in a symplectic representation, namely the braid group Br
n
acts on the first homology group of a genus
g
surface via Dehn twists. Our computations show that such groups have only 2-torsion. We also investigate stabilization properties and provide Poincaré series, for both unstable and stable homology.</description><identifier>ISSN: 0021-2172</identifier><identifier>EISSN: 1565-8511</identifier><identifier>DOI: 10.1007/s11856-019-1832-3</identifier><language>eng</language><publisher>Jerusalem: The Hebrew University Magnes Press</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Braid theory ; Group Theory and Generalizations ; Homology ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Theoretical</subject><ispartof>Israel journal of mathematics, 2019-03, Vol.230 (2), p.653-692</ispartof><rights>The Hebrew University of Jerusalem 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-2d218a782df9237a481fcd743b0c3275b36e98a729cce1ec126cb8d450c448893</citedby><cites>FETCH-LOGICAL-c316t-2d218a782df9237a481fcd743b0c3275b36e98a729cce1ec126cb8d450c448893</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/s11856-019-1832-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11856-019-1832-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Callegaro, Filippo</creatorcontrib><creatorcontrib>Salvetti, Mario</creatorcontrib><title>Homology of the family of hyperelliptic curves</title><title>Israel journal of mathematics</title><addtitle>Isr. J. Math</addtitle><description>Homology of braid groups and Artin groups can be related to the study of spaces of curves. We completely calculate the integral homology of the family of smooth curves of genus
g
with one boundary component, that are double coverings of the disk ramified over
n
= 2
g
+1 points. The main part of such homology is described by the homology of the braid group with coefficients in a symplectic representation, namely the braid group Br
n
acts on the first homology group of a genus
g
surface via Dehn twists. Our computations show that such groups have only 2-torsion. We also investigate stabilization properties and provide Poincaré series, for both unstable and stable homology.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Braid theory</subject><subject>Group Theory and Generalizations</subject><subject>Homology</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Theoretical</subject><issn>0021-2172</issn><issn>1565-8511</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp1kFFLwzAUhYMoWKc_wLeCz5m5N02TPMpQJwx80efQpunW0S41aYX9e7tV8Mmny4HvnAsfIffAlsCYfIwASuSUgaagOFJ-QRIQuaBKAFyShDEEiiDxmtzEuGdMcAk8Icu173zrt8fU1-mwc2lddE17Trtj74Jr26YfGpvaMXy7eEuu6qKN7u73Lsjny_PHak03769vq6cNtRzygWKFoAqpsKo1cllkCmpbyYyXzHKUouS50xOA2loHzgLmtlRVJpjNMqU0X5CHebcP_mt0cTB7P4bD9NIgAtMatconCmbKBh9jcLXpQ9MV4WiAmZMWM2sxkxZz0mL41MG5Eyf2sHXhb_n_0g-5YmNy</recordid><startdate>20190301</startdate><enddate>20190301</enddate><creator>Callegaro, Filippo</creator><creator>Salvetti, Mario</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20190301</creationdate><title>Homology of the family of hyperelliptic curves</title><author>Callegaro, Filippo ; Salvetti, Mario</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-2d218a782df9237a481fcd743b0c3275b36e98a729cce1ec126cb8d450c448893</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Braid theory</topic><topic>Group Theory and Generalizations</topic><topic>Homology</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Callegaro, Filippo</creatorcontrib><creatorcontrib>Salvetti, Mario</creatorcontrib><collection>CrossRef</collection><jtitle>Israel journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Callegaro, Filippo</au><au>Salvetti, Mario</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Homology of the family of hyperelliptic curves</atitle><jtitle>Israel journal of mathematics</jtitle><stitle>Isr. J. Math</stitle><date>2019-03-01</date><risdate>2019</risdate><volume>230</volume><issue>2</issue><spage>653</spage><epage>692</epage><pages>653-692</pages><issn>0021-2172</issn><eissn>1565-8511</eissn><abstract>Homology of braid groups and Artin groups can be related to the study of spaces of curves. We completely calculate the integral homology of the family of smooth curves of genus
g
with one boundary component, that are double coverings of the disk ramified over
n
= 2
g
+1 points. The main part of such homology is described by the homology of the braid group with coefficients in a symplectic representation, namely the braid group Br
n
acts on the first homology group of a genus
g
surface via Dehn twists. Our computations show that such groups have only 2-torsion. We also investigate stabilization properties and provide Poincaré series, for both unstable and stable homology.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11856-019-1832-3</doi><tpages>40</tpages></addata></record> |
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| ispartof | Israel journal of mathematics, 2019-03, Vol.230 (2), p.653-692 |
| issn | 0021-2172 1565-8511 |
| language | eng |
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| subjects | Algebra Analysis Applications of Mathematics Braid theory Group Theory and Generalizations Homology Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical |
| title | Homology of the family of hyperelliptic curves |
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