arXiv subjects

Daniel Stevenson

Publications and source records attributed to Daniel Stevenson.

4 recordsLinked to original sources

arXiv2019

The Weyl map and bundle gerbes

We introduce the notion of a general cup product bundle gerbe and use it to define the Weyl bundle gerbe on T x SU(n)/T. The Weyl map from T x SU(n)/T to SU(n) is then used to show that the pullback of the basic bundle gerbe on SU(n) defined by the second two authors is stably isomorphic to the Weyl bundle gerbe as SU(n)-equivariant bundle gerbes. Both bundle gerbes come equipped with connections and curvings and by considering the holonomy of these we show that these bundle gerbes are not D-stably isomorphic.

math.DG↗

arXiv2013

Circle packing and interpolation in Fock spaces

It was shown by James Tung in 2005 that if a sequence $Z=\{z_n\}$ of points in the complex plane satisfies $$\inf_{n\not=m}|z_n-z_m|>2/\sqrtα,$$ then $Z$ is a sequence of interpolation for the Fock space $F^p_α$. Using results from circle packing, we show that the constant above can be improved to $$\sqrt{2π/(\sqrt3\,α)},$$ which is strictly smaller than $2/\sqrtα$. A similar result will also be obtained for sampling sequences.

math.CV↗

arXiv2001

Yet another construction of the central extension of the loop group

We give a characterisation of central extensions of a Lie group G by the non-zero complex numbers in terms of a differential two-form on G and a differential one-form on GxG. This is applied to the case of the central extension of the loop group.

math.DG↗

arXiv1999

Bundle gerbes: stable isomorphism and local theory

We consider the notion of stable isomorphism of bundle gerbes. It has the consequence that the stable isomorphism classes of bundle gerbes over a manifold M are in bijective correspondence with H^3(M, Z). Stable isomorphism sheds light on the local theory of bundle gerbes and enables us to develop a classifying theory for bundle gerbes using results of Gajer on BC^x bundles.

math.DG↗