The Spectral Flow of the Odd Signature operator and Higher Massey Products

Details The Spectral Flow of the Odd Signature operator and Higher Massey Products The Spectral Flow of the Odd Signature operator and Higher Massey Products

1994-06-30

arxiv.org/abs/dg-ga/9406007v1

Mathematics

Differential Geometry

35 pages, report1

Scientific paper

We show how to compute the spectral flow of the odd signature operator $\pm *d_{a_t}-d_{a_t}*$ along an analytic path of flat connections $a_t$ on a bundle over a closed odd-dimensional manifold in terms of Massey products in the DGLA of bundle-valued differential forms. To obtain this information, we set up a sequence of cochain complexes $\{\calg^*_n,\delta_n\}$, for $n=0,1,2,\ldots$ and Hermitian forms $$Q_n:\calg_n\times\calg_n\ra \bbbC$$ whose signatures determine the spectral flow through $t=0$. The complexes and Hermitian forms are constructed using Massey products.

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