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【期刊论文】MODULAR INVARIANCE AND CHARACTERISTIC NUMBERS
刘克峰, KEFENG LIU
,-0001,():
-1年11月30日
We prove that a general miraculous cancellation formula, the divisibility of certain characteristic numbers and some other topological results are consequences of the modular invariance of elliptic operators on loop space.
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13浏览
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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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39浏览
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80下载
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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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42浏览
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69下载
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刘克峰, Bong H. Lian, Kefeng Liu, and Shing-Tung Yau
,-0001,():
-1年11月30日
We generalize our theorems in Mirror Principle Ⅰ to a class of balloon manifolds. Many of the results are proved for convex projective manifolds. In a subsequent paper, Mirror Principle Ⅲ, we will extend the results to projective manifolds without the convexity assumption.
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76浏览
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119下载
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【期刊论文】ON A PROOF OF A CONJECTURE OF MARINO-VAFA ON HODGE INTEGRALS
刘克峰, CHIU-CHU MELISSA LIU, KEFENG LIU, AND JIAN ZHOU
,-0001,():
-1年11月30日
We outline a proof of a remarkable formula for Hodge integrals conjectured by Mar
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22浏览
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