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Extending topological surgery to natural processes and dynamical systems.
Stathis Antoniou1, Sofia Lambropoulou1
1Department of Mathematics, National Technical University of Athens, Athens, Greece.
Plos One
|September 16, 2017
Summary
Topological surgery, a mathematical method, is extended to model natural phenomena. New concepts like solid and embedded surgery enhance understanding of dynamics in processes from DNA recombination to black hole formation.
Area of Science:
- Mathematics
- Physics
- Biology
Background:
- Topological surgery is a mathematical technique for manifold construction.
- Natural phenomena like DNA recombination and tornado formation exhibit topological changes.
Purpose of the Study:
- To enhance topological surgery with concepts of forces and dynamics.
- To model natural phenomena using extended topological surgery.
Main Methods:
- Extended the formal definition of topological surgery to a continuous process.
- Introduced solid topological surgery for 2D/3D phenomena.
- Developed embedded surgery in S3 for complex spatial interactions.
- Connected concepts to a dynamical system model.
Main Results:
- New theoretical concepts enhance topological surgery.
- Solid and embedded surgery provide models for diverse natural phenomena.
- A dynamical system model is presented for 2D 0-surgery and hole drilling behaviors.
Conclusions:
- The enhanced topological surgery framework offers new insights into natural phenomena.
- This work bridges topology and dynamics for a deeper understanding of manifold transformations.
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