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Research Frontiers in Differential Topology and Smooth Manifolds

Investigates smooth structures on manifolds, characteristic classes, and differential topological invariants relevant to physical systems.

Exotic Structures on High-Dimensional Spheres
Singularities and Smoothing in Cobordism Theory
Stratified Manifolds and Whitney Stratification Dynamics
Transversality Breaking in Intersection Theory
Foliation Rigidity and Ergodic Geometry
Handle Decompositions Beyond Classical Morse Theory
Diffeomorphism Groups and Infinite-Dimensional Symmetry
Characteristic Classes in Non-orientable Fiber Bundles
Spin Structures and Moduli Space Topology
Curvature Constraints on Topological Type

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