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Please use this identifier to cite or link to this item: http://hdl.handle.net/2289/4107
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dc.contributor.authorMajor, Seth A.-
dc.contributor.authorRideout, David-
dc.contributor.authorSurya, Sumati-
dc.date.accessioned2011-08-23T08:05:23Z-
dc.date.available2011-08-23T08:05:23Z-
dc.date.issued2009-09-
dc.identifier.citationClassical and Quantum Gravity, 2009, Vol.26, p175008en
dc.identifier.issn0264-9381-
dc.identifier.issn1361-6382 (Online)-
dc.identifier.urihttp://hdl.handle.net/2289/4107-
dc.descriptionRestricted Access. An open-access version is available at arXiv.org (one of the alternative locations)en
dc.description.abstractWe present a computational tool that can be used to obtain the ‘spatial’ homology groups of a causal set. Localization in the causal set is seeded by an inextendible antichain, which is the analogue of a spacelike hypersurface, and a one-parameter family of nerve simplicial complexes is constructed by ‘thickening’ this antichain. The associated homology groups can then be calculated using existing homology software, and their behaviour studied as a function of the thickening parameter. Earlier analyticalwork showed that for an inextendible antichain in a causal set which can be approximated by a globally hyperbolic spacetime region, there is a one-parameter sub-family of these simplicial complexes which are homological to the continuum, provided the antichain satisfies certain conditions. Using causal sets that are approximated by a set of 2D spacetimes, our numerical analysis suggests that these conditions are generically satisfied by inextendible antichains. In both 2D and 3D simulations, as the thickening parameter is increased, the continuum homology groups tend to appear as the first region in which the homology is constant, or ‘stable’, above the discreteness scale. Below this scale, the homology groups fluctuate rapidly as a function of the thickening parameter. This provides a necessary though not sufficient criterion to test for manifoldlikeness of a causal set.en
dc.language.isoenen
dc.publisherIOP Publishing Ltd.en
dc.relation.urihttp://arxiv.org/abs/0902.0434en
dc.relation.urihttp://dx.doi.org/ 10.1088/0264-9381/26/17/175008en
dc.relation.urihttp://adsabs.harvard.edu/abs/2009CQGra..26q5008Men
dc.rights2009 IOP Publishing Ltd.en
dc.subjectLattice and discrete methodsen
dc.subjectLogic and set theoryen
dc.subjectSpacetime topology, causal structure, spinor structureen
dc.titleStable homology as an indicator of manifoldlikeness in causal set theoryen
dc.typeArticleen
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