Combinatorial Geometry with Application to Field Theory

Motivated by the combinatorial principle, particularly, the CC conjecture, i.e., any mathematical science can be reconstructed from or made by combinatorialization, this book surveys mathematics and field theory.

Topics covered in this book include fundamental of combinatorics, algebraic combinatorics, topology with Smarandache geometry, combinatorial differential geometry, combinatorial Riemannian submanifolds, Lie multi-groups, combinatorial principal fiber bundles, gravitational field, quantum fields and gauge field with their combinatorial generalization, also with discussions on fundamental questions in epistemology.

Nearly all geometries, such as pseudo-manifold geometries, Finsler geometry, combinatorial Finsler geometries, Riemann geometry, combinatorial Riemannian geometries, Weyl geometry, Kahler geometry are particular cases of Smarandache geometries.

All of these materials are valuable for researchers or graduate students in topological graph theory with enumeration, topology, Smarandache geometry, Riemannian geometry, gravitational or quantum fields, many-body system and globally quantifying economy.