کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10735173 | 1044310 | 2005 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The moduli space of torsion-free G2 structures
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The moduli space of torsion-free G2 structures The moduli space of torsion-free G2 structures](/preview/png/10735173.png)
چکیده انگلیسی
Let M be the moduli space of torsion-free G2 structures on a compact oriented G2 manifold M. The natural cohomology map Ï3:MâH3(M,â) is known to be a local diffeomorphism [Compact Manifolds with Special Holonomy, Oxford University Press, 2000]. Let M1âM be the subset of G2 structures with volume (M)=1. We show every nonzero element of H4(M,â)=H3(M,â)* is a Morse function on M1 when composed with Ï3, and we compute its Hessian. The result implies a special case of Torelli's theorem: if H1(M,â)=0 and dimH3(M,â)=2, the cohomology map Ï3:MâH3(M,â) is one to one on each connected component of M. We formulate a compactness conjecture on the set of G2 structures of volume (M)=1 with bounded L2 norm of curvature. If this conjecture were true, it would imply that every connected component of M is contractible, and that every compact G2 manifold supports a G2 structure whose fundamental 4-form represents the negative of the (nonzero) first Pontryagin class of M. We also observe that when H1(M,â)=0, and the volume of the torus H3(M,â)/H3(M,â¤) is constant along M1, the locus Ï3(M1)âH3(M,â) is a hyperbolic affine sphere.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 53, Issue 2, February 2005, Pages 166-179
Journal: Journal of Geometry and Physics - Volume 53, Issue 2, February 2005, Pages 166-179
نویسندگان
Sung Ho Wang,