Differential Topology Assignment Help

Differential Topology Assignment Help

Differential Topology Assignment Help

Topology is a branch in mathematics that deals with properties that are preserved through stretching of objects twisting them and also reforming them.

Topology is used in mathematics in many areas. These areas include ; knot Theory, Riemann surfaces in complex analysis, differential equations, dynamical systems, and many other areas.

The inventor who discovered topology is called George Ferdinand Ludwig Phillip Cantor.

For knowledge purposes, it is important to know that topology is a branch that deals with pure mathematics.

On the other hand, differential topology is a field in mathematics that is associated with differentiable functions. Differential topology has a relationship with differential geometry.

This study deals with differential manifolds.

The combination of differential topology and differential geometry makes up the geometry Theory.

What brings the difference between differential geometry and differential topology is that when it comes differential topology it deals with inherently global problems.

How topology was discovered as a discipline was after the progression relating to Euclid’s n-dimensional space to Gaussian spaces.

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The following is some few differential topology topics that will offer help on

Submersion Lie derivative
Orientability Transversality
Immersion Poincare- Hopf theorem
Submanifolds Differentiable function
Manifolds in RN Differential forms and integration forms
Foliation Whitney embedding theorem
Morse Theory Pontryagin class
Homotopy and stability Chern class
Embedding Spin structure
Saddle point De Rhamcohomology
Derivatives and tangents Hairy ball theorem
Integral curve Smails paradox
Transversality Sards theorem and morse function
Frobenius theorem Smooth maps of manifolds