トポロジー火曜セミナー

過去の記録 ~05/21次回の予定今後の予定 05/22~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
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

2021年07月06日(火)

17:30-18:30   オンライン開催
参加を希望される場合は、セミナーのホームページから参加登録を行って下さい。
窪田 陽介 氏 (信州大学)
Codimension 2 transfer map in higher index theory (JAPANESE)
[ 講演概要 ]
The Rosenberg index is a topological invariant taking value in the K-group of the C*-algebra of the fundamental group, which is a strong obstruction for a closed spin manifold to admit a positive scalar curvature (psc) metric. In 2015 Hanke-Pape-Schick proves that, for a nice codimension 2 submanifold N of M, the Rosenberg index of N obstructs to a psc metric on M. This is a far reaching generalization of a classical result of Gromov and Lawson. In this talk I introduce a joint work with T. Schick and its continuation concerned with this `codimension 2 index' obstruction. We construct a map between C*-algebra K-groups, which we call the codimension 2 transfer map, relating the Rosenberg index of M to that of N directly. This shows that Hanke-Pape-Schick's obstruction is dominated by a standard one, the Rosenberg index of M. We also extend our codimension 2 transfer map to secondary index invariants called the higher rho invariant. As a consequence, we obtain some example of psc manifolds are not psc null-cobordant.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html