already exhibited topology math r n math moreover differential topology restrict necessarily study diffeomorphism example symplectic topology subbranch differential topology studies global properties symplectic manifolds differential geometry concerns problems may local ''or'' global always non trivial local properties thus differential geometry may study differentiable manifolds equipped ''connection'' ''metric'' may riemannian pseudo riemannian finsler special sort ' 'distribution'' cr structure distinction differential geometry differential topology blurred however
Formal science Mathematics Pure mathematics Geometry Differential topology