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For a gerbe Y over a smooth proper Deligne-Mumford stack B banded by a finite group G, we prove a structure result on the Gromov-Witten theory of Y, expressing Gromov-Witten invariants of Y in terms of Gromov-Witten invariants of B twisted by various flat U(1)-gerbes on B. This is interpreted as a Leray-Hirsch type of result for Gromov-Witten theory of gerbes.

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The paper presents a study of Fuglede’s $p$ -module of systems of measures in condensers in polarizable Carnot groups. In particular, we calculate the $p$ -module of measures in spherical ring domains, find the extremal measures, and finally, extend a theorem by Rodin to these groups.

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