ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A generalization of the Dirac string trick for higher-dimensional manifolds is presented. As a rather unexpected result, the procedure is shown to yield homotopy spheres. Because of their relevant interest to physical theories, particular emphasis is given to even-dimensional homotopy spheres. For instance, it is demonstrated that a nontrivial representation of 6–10-dimensional exotic spheres in dimensions 4k+2 can be performed by using the Pontrjagin–Thom construction. The physical content of the results is consistent with Witten's hypothesis [Commun. Math. Phys., 100, 197–229 (1985)] that n–10-dimensional exotic spheres can be interpreted as gravitational instanton and/or soliton. It is also shown that three mutually diffeomorphic elements can be isolated from the 6–10-dimensional exotic spheres and their spectrum is provided.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.529078
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