• Corpus ID: 228063762

Pontrjagin duality on multiplicative Gerbes.

@article{Blanco2020PontrjaginDO,
  title={Pontrjagin duality on multiplicative Gerbes.},
  author={Jaider Blanco and Bernardo Uribe and Konrad Waldorf},
  journal={arXiv: Algebraic Topology},
  year={2020}
}
We use Segal-Mitchison's cohomology of topological groups to define a convenient model for topological gerbes. We introduce multiplicative gerbes over topological groups in this setup and we define its representations. For a specific choice of representation, we construct its category of endomorphisms and we show that it induces a new multiplicative gerbe over another topological group. This new induced group is fibrewise Pontrjagin dual to the original one and therefore we called the pair of… 
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References

SHOWING 1-10 OF 41 REFERENCES

FOUR EQUIVALENT VERSIONS OF NONABELIAN GERBES

We recall and partially expand four versions of smooth, non-abelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all these four versions are

Bundle Gerbes for Chern-Simons and Wess-Zumino-Witten Theories

We develop the theory of Chern-Simons bundle 2-gerbes and multiplicative bundle gerbes associated to any principal G-bundle with connection and a class in H4(BG, ℤ) for a compact semi-simple Lie

Bundle gerbes

. Just as C × principal bundles provide a geometric realisation of two-dimensional integral cohomology; gerbes or sheaves of groupoids, provide a geometric realisation of three dimensional integral

Polyakov-Wiegmann formula and multiplicative gerbes

An unambiguous definition of Feynman amplitudes in the Wess-Zumino-Witten sigma model and the Chern-Simon gauge theory with a general Lie group is determined by a certain geometric structure on the

Categorical Morita Equivalence for Group-Theoretical Categories

A finite tensor category is called pointed if all its simple objects are invertible. We find necessary and sufficient conditions for two pointed semisimple categories to be dual to each other with

The basic gerbe over a compact simple Lie group

Let $G$ be a compact, simply connected simple Lie group. We give a construction of an equivariant gerbe with connection on $G$, with equivariant 3-curvature representing a generator of $H^3_G(G,\Z)$.