A modification of the Hodge star operator on manifolds with boundary

Ryszard L. Rubinsztein Department of Mathematics, Uppsala University

Geometric Analysis and Geometric Topology Rings and Algebras mathscidoc:1701.15005

Arkiv for Matematik, 52, (2), 355-365, 2012.12
For smooth compact oriented Riemannian manifolds$M$of dimension 4$k$+2,$k$≥0, with or without boundary, and a vector bundle$F$on$M$with an inner product and a flat connection, we construct a modification of the Hodge star operator on the middle-dimensional (parabolic) cohomology of$M$twisted by$F$. This operator induces a canonical complex structure on the middle-dimensional cohomology space that is compatible with the natural symplectic form given by integrating the wedge product. In particular, when$k$=0 we get a canonical almost complex structure on the non-singular part of the moduli space of flat connections on a Riemann surface, with monodromies along boundary components belonging to fixed conjugacy classes when the surface has boundary, that is compatible with the standard symplectic form on the moduli space.
No keywords uploaded!
[ Download ] [ 2017-01-08 20:36:38 uploaded by arkivadmin ] [ 685 downloads ] [ 0 comments ]
@inproceedings{ryszard2012a,
  title={A modification of the Hodge star operator on manifolds with boundary},
  author={Ryszard L. Rubinsztein},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203638234704066},
  booktitle={Arkiv for Matematik},
  volume={52},
  number={2},
  pages={355-365},
  year={2012},
}
Ryszard L. Rubinsztein. A modification of the Hodge star operator on manifolds with boundary. 2012. Vol. 52. In Arkiv for Matematik. pp.355-365. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203638234704066.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved