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【期刊论文】Heat Kernels, Symplectic Geometry, Moduli Spaces and Finite Groups
刘克峰, Kefeng Liu
,-0001,():
-1年11月30日
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【期刊论文】Adiabatic Limits and Foliations
刘克峰, Kefeng Liu and Weiping Zhang
,-0001,():
-1年11月30日
We use adiabatic limits to study foliated manifolds. The Bott connection naturally shows up as the adiabatic limit of Levi-Civita connections. As an application, we then construct certain natural elliptic operators associated to the foliation and present a direct geometric proof of a vanshing theorem of Connes[Co], which extends the Lichnerowicz vanishing theorem [L] to foliated manifolds with spin leaves, for what we call almost Riemannian foliations. Several new vanishing theorems are also proved by using our method.
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【期刊论文】Mathematical Results Inspired by Physics
刘克峰, Kefeng Liu
,-0001,():
-1年11月30日
I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of intersection numbers of the moduli spaces of flat connections on a Riemann surface by using heat kernels. (3) The mirror principle about counting curves in Calabi-Yau and general projective manifolds by using hypergeometric series.
Localization,, Elliptic genera,, Moduli spaces,, Mirror principle.,
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70浏览
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刘克峰, Kefeng Liu
,-0001,():
-1年11月30日
In this note we describe some new topological results derived from the modular invariance of certain elliptic operators on loop spaces under the action of SL2(Z). The results include very general rigidity, divisibility and vanishing theorems in topology.
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