# The Dirac operator under collapse to a smooth limit space

#### Autoren: Saskia Roos (2020)

Let (Mi,gi)i∈ℕ be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower-dimensional Riemannian manifold (B, h) in the Gromov–Hausdorff topology. Then, it happens that the spectrum of the Dirac operator converges to the spectrum of a certain first-order elliptic differential operator DB on B. We give an explicit description of DB and characterize the special case where DB equals the Dirac operator on B.

Zeitschrift:
Ann. Glob. Anal. Geom.
Verlag:
Springer
Seiten:
121–151
Band:
57

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