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Lorentzian structures of open, spin manifolds (1989)

Bugajska, Krystyna

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 30 (1989), S. 619-623

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: The possible set of inequivalent Lorentz structures on an open, connected, spin four-manifold M is investigated. Using the Steenrod correspondence between Lorentz metrics and tangent line bundles, the family of all homotopy classes of possible Lorentz structures on M is obtained. This approach allows one to distinguish explicitly between time-orientable and time-nonorientable Lorentzian metrics. Moreover, it is shown that any two inequivalent, time-orientable Lorentzian structures that correspond to generators of the torsionless part of H1(M, Z) can be related to each other by using a Morse function with one nondegenerate critical point of index 1 which describes a surgery of type (1, 3) in some decomposition of M=∪i=1∞ Ui.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.528428

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