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We explicitly construct an SO(2)-action on a skeletal version of the2-dimensional framed bordism bicategory. By the 2-dimensional CobordismHypothesis for framed manifolds, we obtain an SO(2)-action on the core offully-dualizable objects of the target bicategory. This action is shown tocoincide with the one given by the Serre automorphism. We give an explicitdescription of the bicategory of homotopy fixed points of this action, anddiscuss its relation to the classification of oriented 2d topological quantumfield theories.

The Serre automorphism via homotopy actions and the Cobordism Hypothesis for oriented manifolds