Expository Remarks on Three-Dimensional Gravity and Hyperbolic Invariants
A. A. Bytsenko (DF/Uel), M. E. X. Guimaraes (IF/Uff)
TL;DR
This paper explores complex invariants of 3D hyperbolic spaces, focusing on Chern-Simons invariants and their role in quantum gravity path integrals, providing insights into geometric and quantum aspects.
Contribution
It analyzes the contribution of Chern-Simons invariants of irreducible U(n)-flat connections to quantum gravitational path integrals in hyperbolic 3-manifolds.
Findings
Chern-Simons invariants influence quantum gravity calculations
Explicit low-order expansion terms are derived
Connections between hyperbolic geometry and quantum invariants are clarified
Abstract
We consider complex invariants associated with compact real three-dimensional hyperbolic spaces. The contribution of the Chern-Simons invariants of irreducible U(n)-flat connections on hyperbolic fibered manifolds to the low order expansion of the quantum gravitational path integral is analyzed.
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