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− | < | + | <!--<bibitemswithcorrections/>--> |
− | + | <!-- {{#dpl: | |
− | == | + | |namespace=Template |
− | + | |titlematch=%Milnor% | |
− | + | |resultsheader=<h3 id="letter:{{{1}}}">{{{1}}}</h3> | |
− | + | |noresultsheader=<div style="display:none"></div> | |
− | {{beginthm| | + | |shownamespace=false |
+ | |mode=userformat | ||
+ | |listseparators=,\n* [[%PAGE%|[%TITLE%]]] ,, | ||
+ | |includepage=* | ||
+ | |ordermethod=title | ||
+ | }} --> | ||
+ | |||
+ | <stepsectioncounter/> | ||
+ | |||
+ | == File Creation Practice == | ||
+ | |||
+ | [[Media:New_submission.pdf|Click here to access the pdf file]]. | ||
+ | |||
+ | == Testing equation numbering == | ||
+ | <wikitex>; | ||
+ | \begin{equation} \label{eq:1} A = B \end{equation} | ||
+ | Here is a reference to equation \ref{eq:1} | ||
+ | </wikitex> | ||
+ | == Still testing equation numbering == | ||
+ | <wikitex>; | ||
+ | \begin{equation}\label{test} C = D \end{equation} | ||
+ | \ref{test} | ||
+ | </wikitex> | ||
+ | |||
+ | == Lists== | ||
+ | <wikitex>; | ||
+ | <ol style="list-tsyle-type:lower-roman> | ||
+ | <li>Frog</li> | ||
+ | </ol> | ||
+ | |||
+ | $$ A \xrightarrow{f} B$$ | ||
+ | |||
+ | $--$ | ||
+ | </wikitex> | ||
+ | {{beginthm|Theorem|\cite{Penrose&Whitehead&Zeeman1961}}}\label{thm:2.1} | ||
+ | For every compact $m$--dimensional PL-manifold $M$ there exists a PL--embedding $ M \hookrightarrow \R^{2m}$. | ||
{{endthm}} | {{endthm}} | ||
− | + | ||
− | + | {{beginrem|Remark}} | |
− | + | For a good exposition of Theorem \ref{thm:2.1} see also \cite{Rourke&Sanderson1972a|p. 63}. | |
− | {{beginthm| | + | {{endrem}} |
+ | |||
+ | {{beginthm|Theorem|\cite{Whitney1944}}}\label{thm:2.2} | ||
+ | For every closed m--dimensional $C^{\infty}$--manifold $M$ there exists a $C^{\infty}$--embedding $M \hookrightarrow \R^{2m}$. | ||
{{endthm}} | {{endthm}} | ||
+ | |||
+ | {{beginrem|Remark}} | ||
+ | For a more modern exposition see also \cite{Adachi1993|p. 67ff}. | ||
+ | {{endrem}} | ||
+ | |||
+ | \begin{theorem} \label{thm:1} | ||
+ | We have $f \colon X \to Y$ | ||
+ | \end{theorem} | ||
+ | |||
+ | Reference \ref{thm:1} | ||
+ | |||
+ | By Theorem | ||
+ | |||
+ | {{equation|$\alpha$|1.2}} | ||
+ | {{eqref|1.2}} | ||
+ | |||
+ | {{begineq|eqtest|$\alpha$}}<label>qtest</label>{{endeq}} | ||
+ | |||
+ | |||
+ | {{beginthm|Theorem}} | ||
+ | Frog | ||
+ | {{endthm}} | ||
+ | |||
+ | \ref{qtest} | ||
+ | \ref{eqtest} | ||
+ | |||
+ | Here is some text leading up to an equation | ||
+ | {{beginrem| }} | ||
+ | $$ A = B $$ | ||
+ | {{endrem}} | ||
+ | Here is some more text after the equation to see how it looks. | ||
+ | |||
+ | Here is some text leading up to an equation | ||
+ | $$ A = B $$ | ||
+ | Here is some more text after the equation to see how it looks. | ||
+ | |||
+ | :{| border="1" cellpadding="2" class="wikitable" style="text-align:center" | ||
+ | |- | ||
+ | ! 4k !! 8 !! 12 !! 16 !! 20 !! 24 !! 28 !! 32 | ||
+ | |- | ||
+ | ! order bP<sub>4k</sub> | ||
+ | | 2<sup>2</sup>.7 || 2<sup>5</sup>.31 || 2<sup>6</sup>.127|| 2<sup>9</sup>.511|| 2<sup>10</sup>.2047.691 || 2<sup>13</sup>.8191 || 2<sup>14</sup>.16384.3617 | ||
+ | |- | ||
+ | |} | ||
+ | <!-- !! 36 !! 40 !! 44 !! 48 !! 52 !! 56 !! 60 !! 64 |- | ||
+ | || 2<sup></sup>. || 2<sup></sup>. || 2<sup></sup>. || 2<sup></sup>. || 2<sup></sup>. || 2<sup></sup>. || 2<sup></sup>. || 2<sup></sup>. || | ||
+ | --> | ||
+ | |||
+ | :{| border="1" cellpadding="2" class="wikitable" style="text-align:center" | ||
+ | |- | ||
+ | ! k !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 | ||
+ | |- | ||
+ | ! B<sub>k</sub> | ||
+ | | 1/6 || 1/30 || 1/42 || 1/30 || 5/66 || 691/2730 || 7/6 || 3617/510 || | ||
+ | |- | ||
+ | |} | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | :{| border="1" cellpadding="2" class="wikitable" style="text-align:center" | ||
+ | |- | ||
+ | ! Dim n !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 !! 11 !! 12 !! 13 !! 14 !! 15 !! 16 !! 17 !! 18 !! 19 !! 20 | ||
+ | |- | ||
+ | ! order Θ<sub>''n''</sub> | ||
+ | | 1 || 1 || 1 || 1 || 1 || 1 || 28 || 2 || 8 || 6 || 992 || 1 || 3 || 2 || 16256 || 2 || 16 || 16 || 523264 || 24 | ||
+ | |- | ||
+ | !''bP''<sub>''n''+1</sub> | ||
+ | | 1 || 1 || 1 || 1 || 1 || 1 || 28 || 1 || 2 || 1 || 992 || 1 || 1 || 1 || 8128 || 1 || 2 || 1 || 261632 || 1 | ||
+ | |- | ||
+ | !Θ<sub>''n''</sub>/''bP''<sub>''n''+1</sub> | ||
+ | | 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 ||2×2 || 6 || 1 || 1 || 3 || 2 || 2 || 2 || 2×2×2 || 8×2 || 2 || 24 | ||
+ | |- | ||
+ | !π<sub>''n''</sub><sup>''S''</sup>/''J'' | ||
+ | | 1 || 2 || 1 || 1 || 1 || 2 || 1 || 2 || 2×2 || 6 || 1 || 1 || 3 || 2×2 || 2 || 2 || 2×2×2 || 8×2 || 2 || 24 | ||
+ | |- | ||
+ | !index | ||
+ | | - || 2 || - || - || - || 2 || - || - || - || - || - || - || - || 2 || - || - || - || - || - || - | ||
+ | |} | ||
+ | |||
+ | |||
+ | [[Media:Spaceform.tiff|link text]] | ||
+ | |||
+ | |||
+ | $$ f \colon X \to Y $$ | ||
+ | |||
+ | <DPL> | ||
+ | namespace=Main | ||
+ | nottitlematch=Main_Page|Sandbox|Links | ||
+ | ordermethod=lastedit | ||
+ | order=descending | ||
+ | minoredits=exclude | ||
+ | author=%Diarmuid Crowley% | ||
+ | count=10 | ||
+ | </DPL> | ||
+ | |||
+ | Just a fest $f \colon A \to B$. | ||
+ | |||
+ | $\Q$ | ||
+ | |||
+ | |||
+ | {{beginthm|a theorem}} | ||
+ | \label{thma} | ||
+ | {{endthm}} | ||
+ | |||
+ | $\text{Spin}$ | ||
+ | |||
+ | by theorem \ref{thma} | ||
+ | |||
+ | <ol start="9"> | ||
+ | <li>Amsterdam</li> | ||
+ | <li>Rotterdam</li> | ||
+ | <li>The Hague</li> | ||
+ | </ol> | ||
+ | |||
+ | <nowiki>[</nowiki>[[#{{anchorencode:Mess1990}}|Mess1990]]<nowiki>]</nowiki>{{#RefAdd:Mess1990}} | ||
+ | |||
+ | <!-- $\sf{no serifs please}$ --> | ||
+ | |||
+ | $\left( \begin{array}{ll} \alpha & \beta \\ \gamma & \delta \end{array} \right)$ | ||
+ | |||
+ | $f = T$ | ||
+ | |||
+ | $ f : X \to Y$ | ||
+ | |||
+ | $$ f : X \to Y $$ | ||
+ | |||
+ | $\Ker$ | ||
+ | |||
+ | $\mathscr{A}$ $\mathscr{B}$ | ||
+ | |||
+ | \bf{ bold} \it{italic} \em{emphasis} | ||
+ | |||
+ | </wikitex> | ||
+ | |||
+ | [[Image:Foliation.png|thumb|300px|3-dimensional Reeb foliation]] | ||
+ | |||
+ | == Tests == | ||
+ | {{citeD|Ranicki1981}} | ||
+ | {{cite|Milnor1956}} {{cite|Milnor1956|Theorem 1}} {{citeD|Milnor1956}} {{citeD|Milnor1956|Theorem 1}} {{citeD2|Milnor1956|Frog}} | ||
+ | |||
+ | <wikitex>; | ||
{{beginproof}} | {{beginproof}} | ||
− | |||
{{endproof}} | {{endproof}} | ||
− | + | </wikitex> | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | ||
− | + | == Section == | |
+ | === Subsection === | ||
+ | \label{subsection} | ||
+ | Refert to subsection \ref{subsection} | ||
+ | \begin{theorem} \label{thm} | ||
+ | test | ||
+ | \end{theorem} | ||
+ | Refer to theorem \ref{thm} | ||
− | + | == Section == | |
+ | <wikitex>; | ||
− | \ | + | '''$\textup{CW}_0$''' |
+ | |||
+ | An [[map-eds:Manifold Atlas:Projects in the Atlas|inter-Wiki link]]. | ||
+ | |||
+ | Another <ref> Test1 </ref> [[map-eds:Manifold Atlas:Projects in the Atlas|inter-Wiki link]]. | ||
+ | |||
+ | dfa<ref>Test2</ref> | ||
− | |||
− | |||
</wikitex> | </wikitex> | ||
+ | |||
+ | ==Footnotes== | ||
+ | <references/> | ||
+ | ==References== | ||
+ | {{#RefList:}} |
Latest revision as of 08:31, 15 October 2019
The sandbox is the page where you can experiment with the wiki syntax. Feel free to write nonsense or clear the page whenever you want. |
Contents |
1 File Creation Practice
Click here to access the pdf file.
2 Testing equation numbering
Here is a reference to equation 1
3 Still testing equation numbering
4 Lists
- Frog
Theorem 5.1 [Penrose&Whitehead&Zeeman1961]. For every compact $m$--dimensional PL-manifold $M$ there exists a PL--embedding $ M \hookrightarrow \R^{2m}$.
Remark 5.2. For a good exposition of Theorem 5.1 see also [Rourke&Sanderson1972a, p. 63].
Theorem 5.3 [Whitney1944]. For every closed m--dimensional $C^{\infty}$--manifold $M$ there exists a $C^{\infty}$--embedding $M \hookrightarrow \R^{2m}$.
Remark 5.4. For a more modern exposition see also [Adachi1993, p. 67ff].
Theorem 5.5. We have $f \colon X \to Y$
Reference 5.5
By Theorem
{{#addlabel: test}}
Theorem 5.6. Frog
3 \ref{eqtest}
Here is some text leading up to an equation
5.7. $$ A = B $$
Here is some more text after the equation to see how it looks.
Here is some text leading up to an equation $$ A = B $$ Here is some more text after the equation to see how it looks.
4k 8 12 16 20 24 28 32 order bP4k 22.7 25.31 26.127 29.511 210.2047.691 213.8191 214.16384.3617
k 1 2 3 4 5 6 7 8 Bk 1/6 1/30 1/42 1/30 5/66 691/2730 7/6 3617/510
Dim n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 order Θn 1 1 1 1 1 1 28 2 8 6 992 1 3 2 16256 2 16 16 523264 24 bPn+1 1 1 1 1 1 1 28 1 2 1 992 1 1 1 8128 1 2 1 261632 1 Θn/bPn+1 1 1 1 1 1 1 1 2 2×2 6 1 1 3 2 2 2 2×2×2 8×2 2 24 πnS/J 1 2 1 1 1 2 1 2 2×2 6 1 1 3 2×2 2 2 2×2×2 8×2 2 24 index - 2 - - - 2 - - - - - - - 2 - - - - - -
$$ f \colon X \to Y $$
Extension DPL (warning): current configuration allows execution of DPL code from protected pages only.
Just a fest $f \colon A \to B$.
$\Q$
a theorem 5.8.
$\text{Spin}$
by theorem 5.8
- Amsterdam
- Rotterdam
- The Hague
[Mess1990]
$\left( \begin{array}{ll} \alpha & \beta \\ \gamma & \delta \end{array} \right)$
$f = T$
$ f : X \to Y$
$$ f : X \to Y $$
$\Ker$
$\mathscr{A}$ $\mathscr{B}$
bold italic emphasis
</wikitex>
5 Tests
[Ranicki1981] [Milnor1956] [Milnor1956, Theorem 1] [Milnor1956] [Milnor1956, Theorem 1] Frog
Proof.
6 Section
6.1 Subsection
Refert to subsection 7.1
Theorem 7.1. test
Refer to theorem 7.1
7 Section
An inter-Wiki link.
Another [1]; inter-Wiki link.
dfa[2]
8 Footnotes
9 References
- [Adachi1993] M. Adachi, Embeddings and immersions, Translated from the Japanese by Kiki Hudson. Translations of Mathematical Monographs, 124. Providence, RI: American Mathematical Society (AMS), 1993. MR1225100 (95a:57039) Zbl 0810.57001
- [Mess1990] G. Mess, Examples of Poincaré duality groups, Proc. Amer. Math. Soc. 110 (1990), no.4, 1145–1146. MR1019274 (91c:20075) Zbl 0709.57025
- [Milnor1956] J. Milnor, On manifolds homeomorphic to the -sphere, Ann. of Math. (2) 64 (1956), 399–405. MR0082103 (18,498d) Zbl 0072.18402
- [Penrose&Whitehead&Zeeman1961] R. Penrose, J. Whitehead and E. Zeeman, Imbedding of manifolds in Euclidean space., Ann. of Math. 73 (1961) 613–623. MR0124909 (23 #A2218) Zbl 0113.38101
- [Rourke&Sanderson1972a] C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Springer-Verlag, 1972. MR0350744 (50 #3236) Zbl 0477.57003
- [Whitney1944] H. Whitney, The self-intersections of a smooth -manifold in -space, Ann. of Math. (2) 45 (1944), 220–246. MR0010274 (5,273g) Zbl 0063.08237