User:Juan Marquez

kws: surface N_3 surface, Juan Manuel Marquez Bobadilla, Juan Marquez, kid, JMMB, vaquero, mathematician, trigenus, trigénero, topology, topología, low dimensional topology, Stiefel-Whitney surface, superficie de Stiefel-Whitney, 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, matemática,s, tensorólogo, tensorman... ... amalgamated free product, HNN-extension, graph of groups, Bass-Serre theory, topological end, mathemagizian


 * mathoverflow


 * juanmarqz at wordpress there, more poetic... meshica-zapotec

Remember: Topology is a modern branch of mathematics which formalizes the processes of stretching and deforming without tearing, as well as of cutting and pasting to construct new spaces, new geometries...

Neologisms on bundles:


 * I-surface bundle
 * circle-surface bundle
 * surface-circle-bundle
 * I-orbiface bundle
 * circle-orbiface bundle
 * orbiface-circle-bundle


 * $$\scriptstyle I\subset E\to F$$
 * $$\scriptstyle S^1\subset E\to F$$
 * $$\scriptstyle F\subset E\to S^1$$
 * $$\scriptstyle I\subset E\to OF$$
 * $$\scriptstyle S^1\subset E\to OF$$
 * $$\scriptstyle OF\subset E\to S^1$$



cultura


juanmanuel marquezbobadilla

my standard is eom

User:Juan Marquez/Bildnis

).
Juan Manuel Márquez Bobadilla ph.d. candidate at CIMAT and math-lecturer at the Dept. of Mathematics, campus CUCEI, Universidad de Guadalajara.

Thesis: tri-genus and splittings of surface bundles over $$S^1$$ with non-orientable fibers, periodic monodromies
 * Reseach field: low-dimensional topology, 3-manifolds, fiber bundles, Topology change, Seifert homology spheres and plumbed V- manifolds.


 * My 1st article with . It is on trigenus of surface bundles, a kind of 3-manifolds
 * I am a Erdös number four: with and since Fico is #3
 * contacts: juanm@cimat.mx, kidvaquero@yahoo.com


 * wikimedia commons uploads


 * OEIS

OEIS-user

I am...
a Rubik´s fan yes, i just recently learn how to solve it. See my algorithm's version at. It is at a moodle´s module, to enter just check the entrar como invitado (enter as an invited) to see.

Some of "mine"

 * 2-sided
 * tri-genus
 * SFS
 * Alexander trick
 * round function
 * covecteur
 * 3-variedad
 * homeotopy
 * Loop theorem
 * Dehn lemma
 * Sphere theorem
 * Handle decompositions of 3-manifolds

Contributions in S.W. Hawking language here.

Some missing yet

 * Klein surface. As for Riemann surfaces, but allowing that the transition functions can be composed with complex conjugation one can obtains the so called dianalytic structure. This helps to define the Klein surface concept. A profit is that even non-orientable surfaces can have this kind of structure.
 * Refs: Klein. Schiffer and Spencer. Alling and Greenleaf. Szepietowski.


 * Geometrization
 * Geometric structure
 * Light Cone Quantization
 * 1-manifold
 * 2-manifold
 * Regular neighborhood
 * Regular neighbourhood
 * Differential geometry of surfaces
 * I-bundle
 * isotopy class
 * Stiefel-Whitney surface
 * Bass-Serre theory
 * Almost-invariant set
 * cabling conjecture
 * N_3
 * simple loop conjecture

Gastronomy

 * totopo Totopodemaiz.jpg Be'ena'a

es:user:Juan Marquez ia:Usator:Juan Marquez simple:user:Juan Marquez
 * birria
 * ceviche
 * umami

stackrel substitute

 * $$\scriptstyle e\longrightarrow N \longrightarrow^{\!\!\!\!\!\!\!\!\!\beta}\ \, G \longrightarrow^{\!\!\!\!\!\!\!\!\!\alpha}\ \,  H \longrightarrow e$$


 * $$\scriptstyle 1\longrightarrow N \longrightarrow^{\!\!\!\!\!\!\!\beta}\ \, G \longrightarrow^{\!\!\!\!\!\!\!\alpha}\ \,  H \longrightarrow 1$$


 * $$\scriptstyle 0\longrightarrow N \longrightarrow^{\!\!\!\!\!\!\beta}\ \, G \longrightarrow^{\!\!\!\!\!\!\alpha}\ \,  H \longrightarrow 0$$

... seen in semidirect product


 * $$\scriptstyle X \stackrel{f}{\to} Y$$

some humor
You will find (finally) an explanation of what was happening in Rudin's mind when he wrote his famous real analysis book: http://abstrusegoose.com/12



Frak
$$\mathfrak{AaBbCcDdUu}$$

$$\scriptstyle \mathfrak{AaBbCcDdUu}$$

$$\scriptstyle \Sigma$$ $$\Sigma$$ scriptstyle

♥

algebraic, geometrical, topological ends and related stuff

 * User:Juan Marquez/ends
 * User:Juan Marquez/HNN-extensions

columns

 * Teoría de Bass-Serre
 * Teorema de Grushko


 * Teorema de Stallings
 * Grafo de grupos


 * Teorema del Ping-pong
 * HNN-extensión

historics

 * esto fué la 1ra prueba del comando \scriptstyle: $$\scriptstyle G=\langle H, t | t^{-1}Kt=L\rangle$$ allá en wiki-ranchu

thing to push
Analogy in mathematics

Deep analogies in mathematics

Deep analogies in a mathematical science

Deep analogies in a mathematical science or in a science in general

Deep analogies in science

Deep analogies in a science in general

Neil Turok Eqn
$$\Psi=\int\mathrm{e}^{{\frac{1}{h}}\int(\frac{R}{16\pi G}-F^2+\bar{\psi}iD\psi-\lambda\varphi\bar{\psi}\psi+|D\varphi|^2-V(\varphi) )}$$


 * User:Juan Marquez/Bildnis

Be'ena'a
Cloud people

matiliztli

Combinatorial Group Th. key words

 * Otto Schreier
 * free group
 * free product
 * amalgamated product
 * Jakob Nielsen
 * word problem
 * conjugacy problem
 * isomorphism problem
 * Bass-Serre theory
 * Ping-pong lemma
 * Geometric group theory

TOPO
If


 * $$\scriptstyle \pi(U_{1},x_{0})=\langle S_{1}\ |\ R_{1}\rangle\,$$,
 * $$\scriptstyle \pi(U_{2},x_{0})=\langle S_{2}\ |\ R_{2}\rangle\,$$ and
 * $$\scriptstyle \pi(U_{1}\cap U_{2}, x_{0})=\langle S\ |\ R\rangle$$.

then, $$\scriptstyle \pi(X, x_{0})=\langle S_1 \cup S_2\ |\ R_1 \cup R_2 \cup \{ (i_1)_{*}(s)((i_2)_{*}(s))^{-1}, s\in S \}\rangle$$.

Here $$\scriptstyle i_1 : U_1 \cap U_2 \rightarrow U_1 $$ and $$\scriptstyle i_2 : U_1 \cap U_2 \rightarrow U_2 $$ are the natural inclusions, then $$\scriptstyle (i_1)_{*}$$ y $$\scriptstyle (i_2)_{*}$$ are the induced group-morphisms $$\scriptstyle (i_1)_{*} : \pi(U_1 \cup U_2, x_0)  \rightarrow  \pi(U_1, x_0) $$ via $$\scriptstyle [\alpha] \rightarrow (i_1)_{*}([\alpha]):=[i_1 \circ \alpha]$$ and analogously $$\scriptstyle (i_2)_{*} : \pi(U_1 \cup U_2, x_0)  \rightarrow  \pi(U_2, x_0) $$ via $$\scriptstyle [\alpha] \rightarrow (i_2)_{*}([\alpha]):=[i_2 \circ \alpha]$$.