Category Archives: math

my profession

a level surface

A level surface f^{-1}(1) for the function f(x,y,z)=x^2+y^2+z^2-3xyz

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splitting into handlebodies


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Filed under 3-manifold, 3-manifolds, fiber bundle, low dimensional topology

short exact sequence and center

Let us prove:

Let 1\to A\stackrel{f}\to B\stackrel{g}\to B/A\to 1 be a short exact sequence, if the center Z(B/A)=1  then Z(B)<A

Proof:  When x\in Z(B) then g(x)\in Z(B/A), so g(x)=1.

Therefore x\in\ker (g)={\rm im}(f)=A



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Pascal’s Rule and double induction

If S is a set with \#S=n and T\subset S such that \#T=k then there are {n\choose k} different of them.

Follow the link pascalbernoulli for a double induction proof.

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primer parcial, examen de multi

aplicado ayer √


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three jordan two-by-two matrices and exponential


How many three-by-three forms are there?

: )

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made in México

maybe, for the presentation \langle a,b,c\mid a^2=1, b^2=1 , c^2=1\rangle, is this the its Cayley’s graph?Nsub3CayleyGcC

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Filed under algebra, group theory, low dimensional topology, math, topology, word algebra