Abstract
We will classify 2-component non-splittable graph links in S3, each of which is aspherically symmetric, i.e. the exterior admits a periodic homeomorphism which does not extend to a periodic homeomorphism of S3. They can be obtained from spherically symmetric graph links by one or two steps of specific types of iterated cabling. Some of them admit both orientation-preserving and orientation-reversing aspherical symmetries. We will study whether they admit Dehn surgeries which yield 3-manifolds with the induced double symmetries or not.
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