holomorphic trivialization

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• Holomorphic vector bundle — In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is complex manifold and the projection map pi:E o X is holomorphic.Specifically, one requires that the trivialization… …   Wikipedia

• Quillen–Suslin theorem — The Quillen–Suslin theorem, also known as Serre s problem or Serre s conjecture, is a theorem in commutative algebra about the relationship between free modules and projective modules over polynomial rings. Every free module over a ring is… …   Wikipedia

• Line bundle — In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example a curve in the plane having a tangent line at each point determines a varying line: the tangent bundle is a way of organising… …   Wikipedia

• Vector bundle — The Möbius strip is a line bundle over the 1 sphere S1. Locally around every point in S1, it looks like U × R, but the total bundle is different from S1 × R (which is a cylinder instead). In mathematics, a vector bundle is a… …   Wikipedia

• Chern-Simons theory — The Chern Simons theory is a 3 dimensional topological quantum field theory of Schwarz type, developed by Shiing Shen Chern and James Harris Simons. In condensed matter physics, Chern Simons theory describes the topological orderin fractional… …   Wikipedia

• Connection form — In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan …   Wikipedia

• Chern–Simons theory — The Chern–Simons theory is a 3 dimensional topological quantum field theory of Schwarz type, introduced by Edward Witten. It is so named because its action is proportional to the integral of the Chern–Simons 3 form. In condensed matter physics,… …   Wikipedia

• Covering space — A covering map satisfies the local triviality condition. Intuitively, such maps locally project a stack of pancakes above an open region, U, onto U. In mathematics, more specifically algebraic topology, a covering map is a continuous surjective… …   Wikipedia