Compactification, topology change and surgery theory

Details Compactification, topology change and surgery theory Compactification, topology change and surgery theory

2003-02-11

arxiv.org/abs/hep-th/0302072v2

Class.Quant.Grav. 20 (2003) 3093-3106

Physics

High Energy Physics

High Energy Physics - Theory

1+19 pages. LaTeX. 9 associated eps files. Discussion of disconnected case added

Scientific paper

10.1088/0264-9381/20/14/312

We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any topology change in dimensions $\geq 5$ may be achieved via a causally continuous cobordism. This extends the known result for 4 dimensions. Therefore, there is no selection rule for compactification at the level of causal continuity. Theorems from surgery theory and handle theory are seen to be very relevant for understanding topology change in higher dimensions. Compactification via parallelisable cobordisms is particularly amenable to study with these tools.

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