Vipul: 2 revisions

2008-05-18T19:16:48Z

2 revisions

← Older revision	Revision as of 19:16, 18 May 2008
(No difference)

Vipul at 23:46, 26 April 2008

2008-04-26T23:46:20Z

← Older revision		Revision as of 23:46, 26 April 2008
Line 1:		Line 1:
			{{basic fact}}
	==Statement==		==Statement==

Vipul: New page: ==Statement== Suppose $U \subset \mathbb{C}$ is an open subset and $\gamma_1, \gamma_2$ are two smooth curves from $p$ to $q$ that are smoothly...

2008-04-19T21:55:06Z

New page: ==Statement== Suppose <math>U \subset \mathbb{C}</math> is an open subset and <math>\gamma_1, \gamma_2</math> are two smooth curves from <math>p</math> to <math>q</math> that are smoothly...

New page

==Statement==

Suppose <math>U \subset \mathbb{C}</math> is an open subset and <math>\gamma_1, \gamma_2</math> are two smooth curves from <math>p</math> to <math>q</math> that are smoothly homotopic. Suppose <math>V \ni p</math> is an open subset contained inside <math>U</math> and <math>f:V \to \mathbb{C}</math> is a [[holomorphic function]].

Let <math>\gamma_t, t \in [0,1]</math> denote the intermediate curves for the homotopy between <math>\gamma_0</math> and <math>\gamma_1</math>. Then, suppose the following is true:

For every <math>t</math>, we can extend <math>f</math> to a holomorphic function <math>f(t)</math> on an open subset <math>V_t</math> containing <math>\gamma_t</math>

Then any two <math>\gamma_t</math>s agree on the overlap and thus, all the values <math>\gamma_t(q)</math> are equal.

Monodromy theorem - Revision history

Vipul: 2 revisions

Vipul at 23:46, 26 April 2008

Vipul: New page: ==Statement== Suppose U \subset \mathbb{C} is an open subset and \gamma_1, \gamma_2 are two smooth curves from p to q that are smoothly...

Vipul: New page: ==Statement== Suppose $U \subset \mathbb{C}$ is an open subset and $\gamma_1, \gamma_2$ are two smooth curves from $p$ to $q$ that are smoothly...