Questions tagged [eta-invariant]

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eta invariant and spectral flow

We know that for a family of first-order self adjoint elliptic (Fredholm) operator $A_t$, for $t\in [0,1]$ we have the formula $$\eta(A_1)-\eta(A_0)=spfl(A_t)_{t\in[0,1]}+\int^1_0 \omega(s)ds,$$ where ...
5
votes
0answers
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Integrand in equivariant Atiyah-Patodi-Singer index theorem

I am trying to determine the integrand in the equivariant Atiyah-Patodi-Singer index theorem by Donnelli ("Eta invariants for G-spaces") for spin manifolds if one only has isolated fixed points. In "...
7
votes
1answer
299 views

Atiyah-Patodi-Singer for manifolds with cusps

Dear Colleagues and Friends, Please let me know if you are aware of any references to the following question. The classical result of Atiyah, Patodi and Singer tells us that if $W$ is a compact ...