S Carlip 1998 Class. Quantum Grav. 15 2629 doi:10.1088/0264-9381/15/9/010
Dominant topologies in Euclidean quantum gravity
S Carlip
Show affiliationsThe dominant topologies in the Euclidean path integral for quantum gravity differ sharply according to the sign of the cosmological constant. For 
, saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For 
, on the other hand, the path integral is dominated by topologies with extremely complicated fundamental groups; while the contribution of each individual manifold is strongly suppressed, the `density of topologies' grows fast enough to overwhelm this suppression. The value 
is thus a sort of boundary between phases in the sum over topologies. I discuss some implications for the cosmological constant problem and the Hartle-Hawking wavefunction.
- PACS
- MSC
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53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
- Subjects
- Dates
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Issue 9 (September 1998)
Received 28 October 1997
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Dominant topologies in Euclidean quantum gravity
S Carlip 1998 Class. Quantum Grav. 15 2629
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