Sandbox

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.

The user responsible for this page is Philipp Kuehl. No other user may edit this page at present.

1 citing

[Kervaire&Milnor1963] [Kervaire&Milnor1963]

2 Fonts

;

$a > b < c/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_uTuc9U$$\newcommand{\bZ}{\mathbb{Z}} \newcommand{\bR}{\mathbb{R}} \newcommand{\bC}{\mathbb{C}} \newcommand{\bH}{\mathbb{H}} \newcommand{\bQ}{\mathbb{Q}} \newcommand{\bF}{\mathbb{F}} \newcommand{\bN}{\mathbb{N}} \DeclareMathOperator\id{id} % identity map \DeclareMathOperator\Sq{Sq} % Steenrod squares \DeclareMathOperator\Homeo{Homeo} % group of homeomorphisms of a topoloical space \DeclareMathOperator\Diff{Diff} % group of diffeomorphisms of a smooth manifold \DeclareMathOperator\SDiff{SDiff} % diffeomorphism under some constraint \DeclareMathOperator\Hom{Hom} % homomrphism group \DeclareMathOperator\End{End} % endomorphism group \DeclareMathOperator\Aut{Aut} % automorphism group \DeclareMathOperator\Inn{Inn} % inner automorphisms \DeclareMathOperator\Out{Out} % outer automorphism group \DeclareMathOperator\vol{vol} % volume \newcommand{\GL}{\text{GL}} % general linear group \newcommand{\SL}{\text{SL}} % special linear group \newcommand{\SO}{\text{SO}} % special orthogonal group \newcommand{\O}{\text{O}} % orthogonal group \newcommand{\SU}{\text{SU}} % special unitary group \newcommand{\Spin}{\text{Spin}} % Spin group \newcommand{\RP}{\Rr\mathrm P} % real projective space \newcommand{\CP}{\Cc\mathrm P} % complex projective space \newcommand{\HP}{\Hh\mathrm P} % quaternionic projective space \newcommand{\Top}{\mathrm{Top}} % topological category \newcommand{\PL}{\mathrm{PL}} % piecewise linear category \newcommand{\Cat}{\mathrm{Cat}} % any category \newcommand{\KS}{\text{KS}} % Kirby-Siebenmann class \newcommand{\Hud}{\text{Hud}} % Hudson torus \newcommand{\underbar}{\underline} %Classifying Spaces for Families of Subgroups \newcommand{\textup}{\text} \newcommand{\sp}{^}\newcommand{\ZZZ}{\mathbb{Z}}a > b < c$ CM: The connected sum of $\RP^2/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_yAGih4$$\RP^2$ with $T^2ZZZ/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_kX6mPd$$T^2ZZZ$ is homeomorphic to $\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2X/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_SpwxOn$$\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2X$.

HV: The connected sum of $\RP^2/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_MIVhpy$$\RP^2$ with $T^2XXX/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_Os4RtJ$$T^2XXX$ is homeomorphic to $\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2Y/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_e7HBYU$$\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2Y$.

LM: The connected sum of $\RP^2/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_mhQRU6$$\RP^2$ with $T^2YYYY/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_O5rShj$$T^2YYYY$ is homeomorphic to $\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2Z/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_CtvY4v$$\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2Z$.

MF: The connected sum of $\RP^2/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_gDRykJ$$\RP^2$ with $T^2VVVV/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_6CSn1W$$T^2VVVV$ is homeomorphic to $\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2ZZ/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_SXue8a$$\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2ZZ$.

The connected sum of $\RP^2/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_O1W2Fp$$\RP^2$ with $T^2/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_EucRDE$$T^2$ is homeomorphic to $\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2ZZZ/var/www/vhost/map.mpim-bonn.mpg.de/tmp/AppWikiTex/tex_eaHX0T$$\RP^2\mathbin{\sharp}\RP^2\mathbin{\sharp}\RP^2ZZZ$.

3 Tests

[Ranicki1981]

Proof.

$\square$$\square$

frog

4 Section

4.1 Subsection

Refert to subsection 4.1

Theorem 4.1. test

Refer to theorem 4.1

5 Section

$\stackrel{CW^2}{\xrightarrow{\hspace*{0.75cm}}}$$\stackrel{CW^2}{\xrightarrow{\hspace*{0.75cm}}}$

An inter-Wiki link.

Another; inter-Wiki link.

sdfasdfa dfa sdfasf

Template:Ref Poincare complexes are great:

$\displaystyle H_i(X) \cong H^{n-i}(X)$ $$\displaystyle H_i(X) \cong H^{n-i}(X)$$

$\displaystyle \oplus, \bigoplus$ $$\displaystyle \oplus, \bigoplus$$