We construct an integration theory for sc-differential forms on oriented branched ep-subgroupoid for which Stokes’ theorem holds true. The construction is compatible with equivalences between ep-groupoids and so gives rise to an integration theory for branched suborbifolds of polyfolds. Examples are the solutions sets of proper oriented Fredholm sections of strong polyfold bundles for which we obtain invariants this way.
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H. Hofer’s research was partially supported by NSF grant DMS-0603957. K. Wysocki’s research was partially supported by NSF grant DMS-0606588. E. Zehnder’s research was partially supported by TH-project.
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Hofer, H., Wysocki, K. & Zehnder, E. Integration theory on the zero sets of polyfold Fredholm sections. Math. Ann. 346, 139–198 (2010). https://doi.org/10.1007/s00208-009-0393-x