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A branch of topology dealing with topological invariants of manifolds.

A theorem which states that if a Kähler form represents an integral cohomology class on a compact manifold, then it must be a projective Abelian variety.

The four following types of groups, 1. linear groups, 2. orthogonal groups, 3. symplectic groups, and 4. unitary groups, which were studied before more exotic types of groups ...

Abstract Algebra

A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of K-theory: topological ...

For an atomic integral domain R (i.e., one in which every nonzero nonunit can be factored as a product of irreducible elements) with I(R) the set of irreducible elements, the ...

A property of finite simple groups which is known for all such groups.

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...

The exterior derivative of a function f is the one-form df=sum_(i)(partialf)/(partialx_i)dx_i (1) written in a coordinate chart (x_1,...,x_n). Thinking of a function as a ...

A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional ...