| Abstract: |
| We consider on a spin manifold with boundary the twisted Dirac operator $D_A$ with local boundary conditions, possibly coupled to a unitary connection $A$. For suitable values of $m$, we define an analogue of the Dirichlet-to-Neumann map corresponding to $D_A - m$, which we call the boundary conjugation (BC) map. By computing its symbol in dimensions $n \geq 3$, we show that the BC map determines the infinite-order jet of the metric and connection on the boundary in the case $m \neq 0$, when the conformal symmetry of the Dirac equation is broken. We go on to show that a real-analytic Riemannian manifold and twisted spin connection can be recovered from the BC map. Similar results hold in dimension $2$ when the auxiliary connection $A$ is absent. |
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