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Pure Mathematics

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Pure Mathematics

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Research Frontiers in Differential Topology and Manifold Theory

Research on smooth manifolds, characteristic classes, and topological invariants using differential-geometric methods.

Exotic Smoothness and Differential Structure Anomalies
Characteristic Classes Beyond Classical Obstructions
Foliation Singularities and Transverse Dynamics
Gauge Theory and Moduli Space Topology
Concordance Invariants in Higher Dimensions
Stratified Spaces and Intersection Homology
Knotted Surfaces in Four-Dimensional Manifolds
Cobordism Algebras and Universal Invariants
Surgery Theory Beyond Simply Connected Manifolds
Diffeomorphism Groups and Pseudo-Isotopy

All Pure Mathematics PhD categories