Differential Topology by C. H. Taubes.

What is known about manifolds?

Dimensions 4, 5 and greater.

How geometry enters the fray.

Interesting scientific or quantitative thoughts or ideas!

Differential Topology by C. H. Taubes.

What is known about manifolds?

Dimensions 4, 5 and greater.

How geometry enters the fray.

Differential Topology by C. H. Taubes.

Smooth manifolds.

What is known about manifolds?

Dimension 1.

Dimension 2.

Dimension 3.

Differential Topology by C. H. Taubes.

Smooth manifolds.

What is known about manifolds?

Dimension 0.

Differential Topology by C. H. Taubes.

Smooth manifolds.

Algebraic Topology by Burt Totaro, K-Theory.

Generalized cohomology theories.

Conclusion.

Further reading.

Algebraic Topology by Burt Totaro.

Vector bundles and characteristic classes.

Algebraic Topology by Burt Totaro.

Homology groups and the cohomology ring.

Algebraic Topology by Burt Totaro.

Homology groups and the cohomology ring.

Algebraic Topology by Burt Totaro.

Calculations of the fundamental group.

The homotopy groups.

Homology groups and the cohomology ring.

Algebraic Topology by Burt Totaro.

Homotopy groups.