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MR1682214 (2000f:58071) 58J52 (58J28 58J32 58J35) Wojciechowski, Krzysztof P. The $\zeta$-determinant and the additivity of the $ŋ$-invariant on the smooth, self-adjoint Grassmannian. Comm. Math. Phys. 201 (1999), no. 2, 423--444.

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