Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
Vilenkin, Cosmic Strings and Domain Walls , Phys
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Cosmic string networks are constrained to less than ~1% of the energy density using CMB+BAO+SN data, with some models preferring mildly negative densities but no Bayesian evidence favoring them over LambdaCDM.
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Morse-Bott inequalities, Topology Change and Cobordisms to Nothing
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.