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Spectral invariants are, roughly speaking, objects built from the spectrum
(or eigenvalues) of geometric operators defined on Riemannian manifolds.
Examples of spectral invariants include the index, eta invariant (also
called the Atiyah-Patodi-Singer invariant), and zeta-regularized (or
Ray-Singer) determinant. Over the past several years there has been interest
in understanding the behavior of the spectral invariants of Dirac type
operators when the underlying Riemannian manifold is cut into pieces. This
has resulted in the search for gluing or pasting formulas for these
invariants. In this talk I will give an introduction to the spectral
invariants mentioned above, and then I will discuss recent work with Jinsung
Park concerning various "cut and paste" formulas for the spectral
invariants.
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