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We study the topology of some simple infinite dimensional singularitiesarising from spaces of \emph{algebraic formal loops}. We prove that in somesimple cases the natural analogue of nearby cycles cohomology for a function onthe loop space vanishes, and show further that a suitably renormalized versionof the above cohomology produces a simple (non-zero) result.

Topology of Singularities on Algebraic Loop Spaces