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.
Differential topology has a lot of mathematical problems that need a solution and many students find it difficult to understand it.
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The following is some few differential topology topics that will offer help on
|Immersion||Poincare- Hopf theorem|
|Manifolds in RN||Differential forms and integration forms|
|Foliation||Whitney embedding theorem|
|Morse Theory||Pontryagin class|
|Homotopy and stability||Chern class|
|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|