2021 Fiscal Year Final Research Report
Does a compact hyperbolic 4-manifold have a symplectic structure?
| Project/Area Number |
17K14186
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Keywords | 幾何解析 |
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| Outline of Final Research Achievements |
We have investigated the scope of Witten localisation techniques:
First, we studied the relation between the index on manifolds with boundary and domain wall fermions, inspired by lattice gauge theory; and we derived a formula expressing the Atiyah-Patodi-Singer index interms of the eta invariants of domain wall fermion Dirac operators. We also studied mod 2 extensions.
Second, we have studied the orientation of moduli spaces of anti-self-dual metrics.
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| Free Research Field |
幾何解析
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| Academic Significance and Societal Importance of the Research Achievements |
指数定理と格子ゲージ理論を架橋し，Atiyah-Patodi-Singerの指数定理の格子ゲージ理論的定式化に道を開いた．さらに，指数の局所化の射程を探った．第一に，境界付き多様体の指数とドメインウォールフェルミオンとの関係を，物理の格子ゲージ理論に触発され，研究したことがある．その結果，APS指数をドメインウォールフェルミオンのエータ不変量で表す公式を得た．これらの公式のmod 2指数や複素フェルミオンへの拡張も研究した．第二に，反自己双対計量のモジュライ空間の向き付け可能性を判定するためのKR指数の計算がある．
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