Abstract
The work of Ray and Singer that introduced analytic torsion, a kind of determinant of the Laplacian operator in topological and holomorphic settings, is naturally generalized in both settings. The couplings are extended in a direct way in the topological setting to general flat bundles and in the holomorphic setting to bundles with (1,1) connections, which, by using the Newlander-Nirenberg theorem, are seen to be the bundles with both holomorphic and antiholomorphic structures. The resulting natural generalizations of Laplacians are not always self-adjoint, and the corresponding generalizations of analytic torsions are thus not always real-valued. The Cheeger-Müller theorem on equivalence in a topological setting of analytic torsion to classical topological torsion generalizes to this complex-valued torsion. On the algebraic side the methods introduced include a notion of torsion associated to a complex equipped with both boundary and coboundary maps.
Original language | English (US) |
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Pages (from-to) | 133-202 |
Number of pages | 70 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 63 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2010 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics