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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The moduli space of isometry classes of Riemannian structures on a smoothmanifold was emphasized by J.A.Wheeler in his superspace formalism of quantumgravity. A natural question concerning it is: What is a natural topology onsuch moduli space that reflects best quantum fluctuations of the geometrieswithin the Planck's scale? This very question has been addressed by B.DeWittand others. In this article we introduce Gromov's $\varepsilon$-approximationtopology on the above moduli space for a closed smooth manifold. After givingreaders some feel of this topology, we prove that each conformal class in themoduli space is dense with respect to this topology. Implication of thisphenomenon to quantum gravity is yet to be explored. When going further togeneral metric spaces, Gromov's geometries-at-large-scale based on histopologies remind one of K.Wilson's theory of renormalization group. We discusssome features of both and pose a question on whether both can be merged into asingle unified theory.

Quantum fluctuations, conformal deformations, and Gromov's topology --- Wheeler, DeWitt, and Wilson meeting Gromov