A modification of the Hodge star operator on manifolds with boundary
2014 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 52, no 2, 355-365 p.Article in journal (Refereed) Published
For smooth compact oriented Riemannian manifolds M of dimension 4k+2, ka parts per thousand yen0, 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.
Place, publisher, year, edition, pages
2014. Vol. 52, no 2, 355-365 p.
IdentifiersURN: urn:nbn:se:uu:diva-234137DOI: 10.1007/s11512-013-0190-3ISI: 000341733100007OAI: oai:DiVA.org:uu-234137DiVA: diva2:757380