User:Juan Marquez

kws: surface N_3 surface, Stiefel-Whitney surface, superficie de Stiefel-Whitney, Juan Manuel Marquez Bobadilla, Juan Marquez, kid, JMMB, vaquero, mathematician, trigenus, trigénero, topology, topología, low dimensional topology, three-manifold, tres-variedad, surface-bundle, circle-bundle, homeotopía, mapping class group, homeotopy of non-orientable manifolds, abstract embedding, the seven N_3-bundles over the 1-sphere, Universidad de Guadalajara, CIMAT, mathe-mathe, mathe-toon, flecha, TQFT, multilinear, multilineal, covector, banda de mobius, quantum mechanics, matemáticas, tensorólogo, tensor-man, topological end, ends of a group, mathemagizian

Hi, I am a topologist and I will try to pour some of my little knowledge to grow this enterprice...and yes, I am the same as in the wikiversity in spanish.

articles

 * in the Sociedad Matemática Mexicana
 * in the Revista Colombiana de Matemáticas
 * some recent advances on the subjet in spanish (please push entrar como invitado to enter)



$$ \begin{matrix} \begin{align} &V\times V\overset{M}{\longrightarrow}\mathbb{R} \\ &(v,w)\mapsto v'Mw \\ &M_{ij}=M(b_i, b_j) \\ &M\in V^{*}\otimes V^{*} \\ &M=M_{st}\beta^s\otimes\beta^t \\ ~ \\ ~ \end{align}

& \begin{align} &V\times V^{*} \overset{M}{\longrightarrow}\mathbb{R} \\ &(v,f)\mapsto v'Mf' \\ &M_{i}^j=M(b_i, \beta^j) \\ &M\in V^{*}\otimes V \\ &M=M_s^t\beta^s\otimes b_t \\ &M_s^t=M_{su}g^{ut} \\ &MG^{-1} \end{align}

\\

\begin{align} &V^{*}\times V\overset{M}{\longrightarrow}\mathbb{R} \\ &(f,w)\mapsto fMw \\ &M_j^i=M(\beta^i, b_j) \\ &M\in V\otimes V^{*} \\ &M=M_t^s b_s\otimes\beta^t \\ &M_t^s=g^{su}M_{ut} \\ &G^{-1}M \end{align}

& \begin{align} &V^{*}\times V^{*} \overset{M}{\longrightarrow}\mathbb{R} \\ &(f,g)\mapsto fMg' \\ &M^{ij}=M(\beta^i, \beta^j) \\ &M\in V\otimes V \\ &M=M^{st}b_s\otimes b_t \\ &M^{st}=g^{su}M_{uv}g^{vt} \\ &G^{-1}MG^{-1} \end{align} \end{matrix} $$

update
i'm working in the ends of a space concept and here, i'm learning by doing, don't mattering to me if i make mistakes or errors... in spanish is in ... dare to interact!

I just had learned to solve the Rubik's puzzle and... i firmly believe that this serves to makes u more clever in your 3d intuitions, What do u think?


 * I like to wander around my webplaces...



es:Usuario:Juan Marquez