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Monodromy theorem

Index Monodromy theorem

In complex analysis, the monodromy theorem is an important result about analytic continuation of a complex-analytic function to a larger set. [1]

12 relations: Analytic continuation, Complex analysis, Complex logarithm, Continuous function, Disk (mathematics), Encyclopedia of Mathematics, Holomorphic function, Intersection (set theory), MathWorld, Monodromy, PlanetMath, Simply connected space.

Analytic continuation

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Complex logarithm

In complex analysis, a complex logarithm of the non-zero complex number, denoted by, is defined to be any complex number for which.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Disk (mathematics)

In geometry, a disk (also spelled disc).

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Encyclopedia of Mathematics

The Encyclopedia of Mathematics (also EOM and formerly Encyclopaedia of Mathematics) is a large reference work in mathematics.

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Holomorphic function

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.

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Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

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MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

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Monodromy

In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity.

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PlanetMath

PlanetMath is a free, collaborative, online mathematics encyclopedia.

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Simply connected space

In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.

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Analytic continuation along a curve.

References

[1] https://en.wikipedia.org/wiki/Monodromy_theorem

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