English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Let $X$ be a non-compact geometrically finite hyperbolic 3-manifold withoutcusps of rank 1. The deformation space $\mc{H}$ of $X$ can be identified withthe Teichm\"uller space $\mc{T}$ of the conformal boundary of $X$ as the graphof a section in $T^*\mc{T}$. We construct a Hermitian holomorphic line bundle$\mc{L}$ on $\mc{T}$, with curvature equal to a multiple of the Weil-Peterssonsymplectic form. This bundle has a canonical holomorphic section defined by$e^{\frac{1}{\pi}{\rm Vol}_R(X)+2\pi i\CS(X)}$ where ${\rm Vol}_R(X)$ is therenormalized volume of $X$ and $\CS(X)$ is the Chern-Simons invariant of $X$.This section is parallel on $\mc{H}$ for the Hermitian connection modified bythe $(1,0)$ component of the Liouville form on $T^*\mc{T}$. As applications, wededuce that $\mc{H}$ is Lagrangian in $T^*\mc{T}$, and that ${\rm Vol}_R(X)$ isa K\"ahler potential for the Weil-Petersson metric on $\mc{T}$ and on itsquotient by a certain subgroup of the mapping class group. For the Schottkyuniformisation, we use a formula of Zograf to construct an explicit isomorphismof holomorphic Hermitian line bundles between $\mc{L}^{-1}$ and the sixth powerof the determinant line bundle.

Chern-Simons line bundle on Teichm\"uller space