The topological cyclic homology of the dual circle
  We give a new proof of a result of Lazarev, that the dual of the circle $S^1_+$ in the category of spectra is equivalent to a strictly square-zero extension as an associative ring spectrum. As an application, we calculate the topological cyclic homology of $DS^1$ and rule out a Koszul-dual reformulation of the Novikov conjecture. 
Cary Malkiewich
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