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
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:
cultura
juanmanuel marquezbobadilla
my standard is
eom
User:Juan Marquez/Bildnis
/meː.ɕiʔ.ko/ ).
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
{\displaystyle S^{1}}
with
non-orientable fibers, periodic
monodromies
wikimedia commons uploads
[3]
OEIS-user
I am...
a Rubik´s fan
yes, i just recently learn how to solve it. See my algorithm's version at
[4] . It is at a
moodle ´s module, to enter just check the entrar como invitado (enter as an invited) to see.
Some of "mine"
Contributions in S.W. Hawking language
here .
Some missing yet
Gastronomy
stackrel substitute
e
⟶
N
⟶
β
G
⟶
α
H
⟶
e
{\displaystyle \scriptstyle e\longrightarrow N\longrightarrow ^{\!\!\!\!\!\!\!\!\!\beta }\ \,G\longrightarrow ^{\!\!\!\!\!\!\!\!\!\alpha }\ \,H\longrightarrow e}
1
⟶
N
⟶
β
G
⟶
α
H
⟶
1
{\displaystyle \scriptstyle 1\longrightarrow N\longrightarrow ^{\!\!\!\!\!\!\!\beta }\ \,G\longrightarrow ^{\!\!\!\!\!\!\!\alpha }\ \,H\longrightarrow 1}
0
⟶
N
⟶
β
G
⟶
α
H
⟶
0
{\displaystyle \scriptstyle 0\longrightarrow N\longrightarrow ^{\!\!\!\!\!\!\beta }\ \,G\longrightarrow ^{\!\!\!\!\!\!\alpha }\ \,H\longrightarrow 0}
... seen in
semidirect product
X
→
f
Y
{\displaystyle \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
[5]
Frak
A
a
B
b
C
c
D
d
U
u
{\displaystyle {\mathfrak {AaBbCcDdUu}}}
A
a
B
b
C
c
D
d
U
u
{\displaystyle \scriptstyle {\mathfrak {AaBbCcDdUu}}}
Σ
{\displaystyle \scriptstyle \Sigma }
Σ
{\displaystyle \Sigma }
scriptstyle
♥
algebraic, geometrical, topological ends and related stuff
columns
historics
esto fué la 1ra prueba del comando \scriptstyle:
G
=
⟨
H
,
t
|
t
−
1
K
t
=
L
⟩
{\displaystyle \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
Ψ
=
∫
e
1
h
∫
(
R
16
π
G
−
F
2
+
ψ
¯
i
D
ψ
−
λ
φ
ψ
¯
ψ
+
|
D
φ
|
2
−
V
(
φ
)
)
{\displaystyle \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 ))}}
Be'ena'a
Cloud people
[6]
matiliztli
Combinatorial Group Th. key words
TOPO
If
π
(
U
1
,
x
0
)
=
⟨
S
1
|
R
1
⟩
{\displaystyle \scriptstyle \pi (U_{1},x_{0})=\langle S_{1}\ |\ R_{1}\rangle \,}
,
π
(
U
2
,
x
0
)
=
⟨
S
2
|
R
2
⟩
{\displaystyle \scriptstyle \pi (U_{2},x_{0})=\langle S_{2}\ |\ R_{2}\rangle \,}
and
π
(
U
1
∩
U
2
,
x
0
)
=
⟨
S
|
R
⟩
{\displaystyle \scriptstyle \pi (U_{1}\cap U_{2},x_{0})=\langle S\ |\ R\rangle }
.
then,
π
(
X
,
x
0
)
=
⟨
S
1
∪
S
2
|
R
1
∪
R
2
∪
{
(
i
1
)
∗
(
s
)
(
(
i
2
)
∗
(
s
)
)
−
1
,
s
∈
S
}
⟩
{\displaystyle \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
i
1
:
U
1
∩
U
2
→
U
1
{\displaystyle \scriptstyle i_{1}:U_{1}\cap U_{2}\rightarrow U_{1}}
and
i
2
:
U
1
∩
U
2
→
U
2
{\displaystyle \scriptstyle i_{2}:U_{1}\cap U_{2}\rightarrow U_{2}}
are the natural inclusions,
then
(
i
1
)
∗
{\displaystyle \scriptstyle (i_{1})_{*}}
y
(
i
2
)
∗
{\displaystyle \scriptstyle (i_{2})_{*}}
are the induced group-morphisms
(
i
1
)
∗
:
π
(
U
1
∪
U
2
,
x
0
)
→
π
(
U
1
,
x
0
)
{\displaystyle \scriptstyle (i_{1})_{*}:\pi (U_{1}\cup U_{2},x_{0})\rightarrow \pi (U_{1},x_{0})}
via
α
→
(
i
1
)
∗
(
α
)
:=
i
1
∘
α
{\displaystyle \scriptstyle [\alpha ]\rightarrow (i_{1})_{*}([\alpha ]):=[i_{1}\circ \alpha ]}
and analogously
(
i
2
)
∗
:
π
(
U
1
∪
U
2
,
x
0
)
→
π
(
U
2
,
x
0
)
{\displaystyle \scriptstyle (i_{2})_{*}:\pi (U_{1}\cup U_{2},x_{0})\rightarrow \pi (U_{2},x_{0})}
via
α
→
(
i
2
)
∗
(
α
)
:=
i
2
∘
α
{\displaystyle \scriptstyle [\alpha ]\rightarrow (i_{2})_{*}([\alpha ]):=[i_{2}\circ \alpha ]}
.