The Spectral Flow of the Odd Signature Operator and Higher Massey Products
نویسنده
چکیده
Let EC denote the complexified adjoint Lie-algebra bundle associated to P . For the purposes of this summary, we will assume that E = EC; the more general case will be dealt with in section 7. Let dt : Ω (M ;EC)→Ω (M ;EC) denote the exterior derivative corresponding to At for each t. At t = 0, we wish to calculate the dimension of ker(D0), which gives the number of eigenvalues λα(t) of Dt passing through 0 at t = 0. Then, for each of these λα(t) which vanish at t = 0, we need to calculate the first non-vanishing derivative of λα(t) at t = 0. Because the analyticity of At implies that each λα(t) is analytic, this information will give a complete description of the spectral flow of Dt near t = 0.
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