On the Quillen determinant

Details On the Quillen determinant On the Quillen determinant

2003-09-07

arxiv.org/abs/math/0309127v1

Mathematics

Differential Geometry

11 pages, to appear in the Journal of Geometry and Physics

Scientific paper

10.1016/j.geomphys.2003.07.001

We explain the bundle structures of the {\it Determinant line bundle} and the {\it Quillen determinant line bundle} considered on the connected component of the space of Fredholm operators including the identity operator in an intrinsic way. Then we show that these two are isomorphic and that they are non-trivial line bundles and trivial on some subspaces. Also we remark a relation of the {\it Quillen determinant line bundle} and the {\it Maslov line bundle}.

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