manifolds and cobordisms

cobordism theory, Introduction

locally Euclidean space

coordinate chart, coordinate transformation

atlas,

smooth structure

manifold

topological manifold

differentiable manifold, ,smooth manifold

infinite dimensional manifold

tangent bundle

normal bundle

G-structure, torsion of a G-structure

Cartan geometry:

Riemannian manifold

complex manifold

symplectic manifold

cobordism

B-bordism

extended cobordism

cobordism category

(∞,n)-category of cobordisms

Thom spectrum

cobordism ring

genus

signature genus, Kervaire invariant

A-hat genus, Witten genus

Whitney embedding theorem

Thom's transversality theorem

Pontrjagin-Thom construction

Galatius-Tillmann-Madsen-Weiss theorem

geometrization conjecture,

Poincaré conjecture

elliptization conjecture

cobordism hypothesis-theorem

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A manifold is called closed if it is

compact;

without boundary.