\begin{tikzpicture}[sketch]

%KREIS P (KP)
\draw[align=center](2,2) circle (1)node{$\bullet P$ \\$L_-^{\uparrow}$};

%KREIS 1 (K1)
\draw[align=center](-2,2) circle (1)node{$\bullet \mathbb{1}$ \\ $L_+^{\uparrow}$};
	%roter Kreis
	\draw[awesome](-2,2) circle(1.1);
	
	%grüner Pfad
	\draw[teal](2,3.2)--(-2,3.2) arc(90:270:1.2)--(2,0.8) arc(-90:90:1.2);
	
	%Blauer Pfad
		%Hilfslinie
		\draw[line width=1mm, white](-3.3,2) arc (180:-0:1.3)--(-0.7,-2);
	\draw[dodgerblue](-3.3,2) arc(180:0:1.3)--(-0.7,-2) arc(-0:-180:1.3)--(-3.3,2);
	
	%orangener Pfad
		%Hilfslinie
		\draw[line width=1mm, white]($(-2,2)+(45:1.4)$) arc(45:225:1.4)--($(2,-2)+(-135:1.4)$) arc(-135:45:1.4)--($(-2,2)+(45:1.4)$);
	\draw[orange]($(-2,2)+(45:1.4)$) arc(45:225:1.4)--($(2,-2)+(-135:1.4)$) arc(-135:45:1.4)--($(-2,2)+(45:1.4)$);
	
	%Pfeil zwischen K1 und KT
		%Hilfslinie
		\draw[line width=1mm,<->, white](-2,-0.9)--(-2,0.875);
	\draw[<->](-2,-0.9)--(-2,0.85);
	\node[right] at (-2,0){T};

%KREIS T (KT)
\draw[align=center](-2,-2) circle (1)node{$\bullet T$ \\$L_-^{\downarrow}$};

	%PFeil zwischen KT und KPT
		%Hilfslinie
		\draw[line width=1mm,<->, white](-0.98,-2)--(0.98,-2);
	\draw[<->](-0.9,-2)--(0.9,-2);
	\node[above] at (0.1,-2){P};
	
%KREIS PT (KPT)
\draw[align=center](2,-2) circle (1)node{$\bullet PT$ \\$L_+^{\downarrow}$};
	
	%Pfeil zwischen KPT und KP
		%Hilfslinie
		\draw[line width=1mm,<->, white](2,-0.98)--(2,0.98);
	\draw[<->](2,-0.9)--(2,0.9);
	\node[right] at (2,0){T};
	
	%Pfeil zwischen KP und K1
		%Hilfslinie
		\draw[line width=1mm,<->, white](-0.875,2)--(0.9,2);
	\draw[<->](-0.85,2)--(0.9,2);
	\node[above] at (0,2){P};


    \node[left, align=right, awesome] at (-4,2){proper orthochronous\\Lorentz Group\\(restricted LG)\\$L_+^\uparrow=\mathrm{SO}^+(1,3)$};
\node[left, align=right, dodgerblue] at (-4,0){orthochorous LG}; 

\node[right, align=left, orange] at (4,-2){proper LG\\$L_+=\mathrm{SO}(1,3)$};
\node[right, align=left, teal] at (4,2){orthochronous LG\\$L^\uparrow=\mathrm{O}^+(1,3)$};
\node[below, teal] at (0,3.2){$L^{\uparrow}$};
\node[right, dodgerblue] at (-3.3,0){L$_0$};
\node[orange] at (20:1.2){$L_+$};

\node  at (0,-5){%
    $L_{\pm}^{\uparrow/ \downarrow}%
    \begin{cases}%
        \uparrow\;&\text{no time inversion (sign $\tensor{\Lambda}{^0_0}=+1$)}\\%
        \downarrow\;&\text{time inversion (sign $\tensor{\Lambda}{^0_0}=-1$)}\\%
        +\;&\det\Lambda=+1\;\text{(proper)}\\%
        -\;&\det\Lambda=-1\;\text{(improper)}%
    \end{cases}$%
};
%\node[align=left]  at (1,-5){$\uparrow=$ no time inversion \\ $\downarrow=$ time inversion};
%\node[align=left] at (-1,-5){$+= \det \Lambda =+1$ (proper) \\ $-=\det \Lambda=-1$ (improper)};
%\node[above]  at (7:9){sign $\Lambda_0^0=+1 $};
%\node[below]  at (3:9){sign $\Lambda_0^0=-1 $};
	
\end{tikzpicture}