The paper attempts to define a T-equivariant complex orientation for K-theory via a formal group law, but the proof has a load-bearing algebraic sign error.
Swan-Tate cohomology of meromorphic circle actions
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abstract
We propose a toy model for symmetry-breaking or bubbling, in terms of cobordism of manifolds with circle actions free on a possible boundary. The Swan-Tate cohomology $t_\T E$ of a complex-oriented $E_\infty$ ring-spectrum $E$ is the extension of a Hopf algebra by its dual, which provides an algebraic rigidification of geometric interest. This note reviews the cases $E = H,K$ and $MU$, with special attention to $\lambda$-ring structures.
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On a complex topological orientation for circle-equivariant K-theory
The paper attempts to define a T-equivariant complex orientation for K-theory via a formal group law, but the proof has a load-bearing algebraic sign error.