14/06/08 05:33:04.15
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著者
URLﾘﾝｸ(www.researchgate.net)
Torsten Asselmeyer-Maluga PhD Researcher
German Aerospace Center (DLR)
About
The differential or smoothness structure of a topological manifold (if it exists) can be non-unique.
In all dimension except 4 there are only a finite number of different (i.e. non-diffeomorphic) smoothness structures.
But dimension 4 is exceptional.
Here there are an infinite number of different smoothness structures,
countable infinite for most compact and uncountable many for many non-compact 4-manifolds.
But what is the physical meaning of this fact, that is my main research program.
URLﾘﾝｸ(en.wikipedia.org)
Carl Henry Brans (born December 13, 1935) is an American mathematical physicist
best known for his research into the theoretical underpinnings of gravitation elucidated in his most widely publicized work, the Brans–Dicke theory.
Recently Brans began study of developments in differential topology concerning the existence of exotic (non-standard) global differential structures and their possible applications to physics.
This work includes looking at the exotic 7-sphere of Milnor as an exotic Yang-Mills bundle,
and most especially the infinity of exotic differential structure on Euclidean four space (exotic R4) as alternative models for space-time in general relativity.
Much of this work has been done in collaboration with Torsten Asselmeyer-Maluga of Berlin.
In particular, they made the proposal that exotic smoothness structures can be resolve some of the problems in cosmology like dark matter or dark energy.
Together they published a book, Exotic Smoothness and Physics World Scientific Press, 2007.