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Title: On recovering continuum topology from a causal set
Authors: Major, Seth A.
Rideout, David
Surya, Sumati
Keywords: quantum gravity
space-time configurations
set theory
Issue Date: Mar-2007
Publisher: American Institute of Physics
Citation: Journal of Mathematical Physics, 2007, Vol.48, 032501
Abstract: An important question that discrete approaches to quantum gravity must address is how continuum features of space-time can be recovered from the discrete substructure. Here, we examine this question within the causal set approach to quantum gravity, where the substructure replacing the space-time continuum is a locally finite partial order. A new topology on causal sets using “thickened antichains” is constructed. This topology is then used to recover the homology of a globally hyperbolic space-time from a causal set which faithfully embeds into it at sufficiently high sprinkling density. This implies a discrete-continuum correspondence which lends support to the fundamental conjecture or “Hauptvermutung” of causal set theory.
Description: Open Access
ISSN: E-ISSN: 1089-7658
P-ISSN: 0022-2488
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Copyright: 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
Appears in Collections:Research Papers (TP)

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