@article{Roos2019, author = {Roos, Saskia}, title = {The Dirac operator under collapse to a smooth limit space}, series = {Annals of global analysis and geometry}, volume = {57}, journal = {Annals of global analysis and geometry}, number = {1}, publisher = {Springer}, address = {Dordrecht}, issn = {0232-704X}, doi = {10.1007/s10455-019-09691-8}, pages = {121 -- 151}, year = {2019}, abstract = {Let (M-i, g(i))(i is an element of 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 D-B on B. We give an explicit description of D-B and characterize the special case where D-B equals the Dirac operator on B.}, language = {en} }