English

On the Quillen determinant

Differential Geometry 2009-11-10 v1 Functional Analysis

Abstract

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}.

Keywords

Cite

@article{arxiv.math/0309127,
  title  = {On the Quillen determinant},
  author = {Kenro Furutani},
  journal= {arXiv preprint arXiv:math/0309127},
  year   = {2009}
}

Comments

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