2003/02/28 by Sean A. Hartnoll, Sean A Hartnoll
Physics and Astronomy · #Black Holes and Theoretical Physics #Causal structure #Compactification (mathematics) #General topology #Noncommutative and Quantum Gravity Theories #Quantum #Quantum Electrodynamics and Casimir Effect #Spacetime #Spacetime topology #Topology (electrical circuits) #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/20/14/312
published as Class.Quant.Grav. 20 (2003) 3093-3106 · 1+19 pages. LaTeX. 9 associated eps files. Discussion of disconnected case added
openalex publication_date 2003/06/23 · arxiv created 2003/06/28 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 ⩾5 may be achieved via a causally continuous cobordism. This extends the known result for four 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 parallelizable cobordisms is particularly amenable to study with these tools.