トポロジー火曜セミナー
過去の記録 ~11/07|次回の予定|今後の予定 11/08~
開催情報 | 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室 |
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担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也 |
セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2008年11月11日(火)
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Thomas Andrew Putman 氏 (MIT)
The second rational homology group of the moduli space of curves
with level structures
Tea: 16:00 - 16:30 コモンルーム
Thomas Andrew Putman 氏 (MIT)
The second rational homology group of the moduli space of curves
with level structures
[ 講演概要 ]
Let $\\Gamma$ be a finite-index subgroup of the mapping class
group of a closed genus $g$ surface that contains the Torelli group. For
instance, $\\Gamma$ can be the level $L$ subgroup or the spin mapping class
group. We show that $H_2(\\Gamma;\\Q) \\cong \\Q$ for $g \\geq 5$. A corollary
of this is that the rational Picard groups of the associated finite covers
of the moduli space of curves are equal to $\\Q$. We also prove analogous
results for surface with punctures and boundary components.
Let $\\Gamma$ be a finite-index subgroup of the mapping class
group of a closed genus $g$ surface that contains the Torelli group. For
instance, $\\Gamma$ can be the level $L$ subgroup or the spin mapping class
group. We show that $H_2(\\Gamma;\\Q) \\cong \\Q$ for $g \\geq 5$. A corollary
of this is that the rational Picard groups of the associated finite covers
of the moduli space of curves are equal to $\\Q$. We also prove analogous
results for surface with punctures and boundary components.