de Rham Cohomology
de Rham cohomology is a formal set-up for the analytic problem: If you have a Differentialk-Form 
on a Manifold 
, is it the Exterior Derivative of another Differential k-Form 
? Formally, if 
then 
. This is more commonly statedas 
, meaning that if is to be the Exterior Derivative of a Differential k-Form, a Necessary condition that must satisfy is that its ExteriorDerivative is zero.
de Rham cohomology gives a formalism that aims to answer the question, ``Are all differential 
-forms on a Manifoldwith zero Exterior Derivative the Exterior Derivatives of 
-forms?'' Inparticular, the th de Rham cohomology vector space is defined to be the space of all -forms with ExteriorDerivative 0, modulo the space of all boundaries of -forms. This is the trivial Vector Space Iff theanswer to our question is yes.
The fundamental result about de Rham cohomology is that it is a topological invariant of the Manifold, namely: theth de Rham cohomology Vector Space of a Manifold is canonically isomorphic to theAlexander-Spanier Cohomology Vector Space 
(also called cohomology with compact support). Inthe case that is compact, Alexander-Spanier Cohomology is exactly singular cohomology.
- Muirhead's Theorem
- Muller's Method
- Mulliken Symbols
- Multiamicable Numbers
- Multifactorial
- Multifractal Measure
- Multigrade Equation
- Multilinear
- Multimagic Series
- Multimagic Square
- Multinomial Coefficient
- Multinomial Distribution
- Multinomial Series
- Multinomial Theorem
- Multiperfect Number
- Multiple Integral
- Multiple Regression
- Multiplication
- Multiplication Magic Square
- Multiplication Principle
- Multiplication Sign
- Multiplication Table
- Multiplicative Character
- Multiplicative Digital Root
- Multiplicative Function