I have a partial drawing which I can't complete right now due to time constraints. I will however provide you with the source material and the method. First, the result:

Second, the code
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\begin{document}
\definecolor{c969696}{RGB}{150,150,150}
\begin{tikzpicture}[y=0.80pt, x=0.80pt, yscale=-1.000000, xscale=1.000000, inner sep=0pt, outer sep=0pt]
\path[fill=black,line join=miter,line cap=butt,line width=0.800pt]
(136.0000,309.3622) node[above right] (text7388) {};
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=1.600pt] (77.5000,207.3622) .. controls (77.5000,207.3622) and
(110.0000,190.9336) .. (148.5714,205.2193) .. controls (187.1429,219.5051) and
(208.7425,214.4305) .. (223.6940,203.7295) .. controls (233.6455,203.3856) and
(228.5209,245.6607) .. (228.7373,255.3927) .. controls (241.8109,255.1247) and
(229.6429,260.9336) .. (229.6429,260.9336) .. controls (229.6429,260.9336) and
(189.2857,273.4336) .. (155.0000,257.3622) .. controls (120.7143,241.2908) and
(87.5000,261.6479) .. (87.5000,261.6479) .. controls (62.3709,241.8132) and
(67.6883,224.4083) .. (77.5000,207.3622) -- cycle;
%%%%%%%%% DASHED LINES
\path[draw=black,dash pattern=on 9.54pt off 9.54pt,line join=miter,line
cap=butt,miter limit=1.00,even odd rule,line width=0.795pt]
(192.1789,264.9757) .. controls (204.8876,266.3769) and (204.5955,215.0655) ..
(192.6842,214.6613) -- (192.6842,214.6613) -- (192.6842,214.6613);
\path[draw=black,dash pattern=on 9.34pt off 9.34pt,line join=miter,line
cap=butt,miter limit=1.00,even odd rule,line width=0.779pt]
(139.1379,251.9081) .. controls (151.8670,253.2510) and (151.5745,204.0758) ..
(139.6440,203.6884) -- (139.6440,203.6884) -- (139.6440,203.6884);
%%%%%%%%%% ARROWS
\path[->,draw=black,line join=miter,line cap=butt,even odd rule,line width=0.800pt]
(85.2064,198.8843) .. controls (94.9900,193.8625) and (116.2613,191.8955) ..
(129.0470,196.0559);
\path[->,draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=0.800pt] (70.7485,255.6590) .. controls (61.4904,246.2335) and
(59.2061,224.9889) .. (68.4835,211.7704);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=1.600pt] (94.7523,234.2397) .. controls (99.2549,215.8434) and
(111.4350,211.0672) .. (127.9863,209.4909);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=1.600pt] (108.5409,241.3107) .. controls (115.4510,226.6988)
and (123.3950,219.7274) .. (138.5929,220.4511);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=1.600pt] (100.4092,208.4303) .. controls (118.7277,206.4666)
and (130.3307,218.6267) .. (135.4110,234.5932);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=1.600pt] (87.3277,220.0975) .. controls (106.6494,218.1132)
and (117.6898,228.9131) .. (123.3901,245.1998);
%%%% Ellipse
\path[draw=black,fill=c969696,line join=round,line cap=round,miter
limit=4.00,line width=1.600pt] (228.2945,231.2868) ellipse (0.3993cm and
0.8303cm);
\path[xscale=0.963,yscale=1.038,fill=black,line join=miter,line cap=butt,line
width=0.800pt] (101.3132,184.9408) node[above right] (text7156) {$\tau$};
\path[xscale=0.963,yscale=1.038,fill=black,line join=miter,line cap=butt,line
width=0.800pt] (52.7323,228.9850) node[above right] (text7162) {$\sigma$};
\path[xscale=0.963,yscale=1.038,fill=black,line join=miter,line cap=butt,line
width=0.800pt] (139.2488,255.7794) node[above right] (text7166) {$\tau_1$};
\path[xscale=0.963,yscale=1.038,fill=black,line join=miter,line cap=butt,line
width=0.800pt] (197.3631,267.3572) node[above right] (text7170) {$\tau_2$};
\path[fill=black,line join=miter,line cap=butt,line width=0.800pt]
(274.0000,238.3622) node[above right] (text7384) {$+$};
\path[cm={{0.0,1.0,-1.0,0.0,(0.0,0.0)}},fill=black,line join=miter,line
cap=butt,line width=0.800pt] (279.1168,-135.8970) node[above right] (text7392)
{$=$};
\path[cm={{0.0,1.0,-1.0,0.0,(0.0,0.0)}},fill=black,line join=miter,line
cap=butt,line width=0.800pt] (310.1168,-449.8970) node[above right] (text7396)
{$=$};
\path[draw=black,line join=round,line cap=butt,miter limit=4.00,line
width=1.600pt] (139.0000,422.3622) ellipse (2.0602cm and 2.1167cm);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=1.600pt] (126.0000,376.8622) .. controls (155.2079,375.3357)
and (182.8903,392.2794) .. (189.5000,421.3622);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=1.600pt] (179.5000,379.3622) .. controls (156.9263,385.7430)
and (143.0268,396.4286) .. (135.0000,419.3622);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=1.600pt] (185.5000,392.3622) .. controls (165.0696,397.9739)
and (153.6168,409.2724) .. (146.0000,427.3622);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,even odd
rule,line width=1.600pt] (174.4759,416.3600) .. controls (171.2596,393.2586)
and (148.1356,388.9491) .. (128.5029,389.8962);
%%%%% dashed pattern
\path[draw=black,dash pattern=on 9.97pt off 9.97pt,line join=miter,line
cap=butt,miter limit=4.00,even odd rule,line width=0.831pt]
(136.6636,347.8792) .. controls (103.8299,350.8115) and (107.5788,492.0596) ..
(142.5002,496.8452);
\path[draw=black,dash pattern=on 9.60pt off 9.60pt,line join=miter,line
cap=butt,miter limit=4.00,even odd rule,line width=0.800pt]
(176.0000,357.3622) .. controls (193.9175,369.8639) and (198.6504,468.7237) ..
(174.5000,488.3622);
%%%% arrows
\path[->,draw=black,line join=miter,line cap=butt,even odd rule,line width=0.800pt]
(89.0000,358.3622) .. controls (120.2581,338.8624) and (151.0718,333.1351) ..
(181.0000,354.8622);
\path[xscale=0.963,yscale=1.038,fill=black,line join=miter,line cap=butt,line
width=0.800pt] (106.5045,328.9305) node[above right] (text7438) {$\tau$};
\path[->, draw=black,line join=miter,line cap=butt,even odd rule,line width=0.800pt]
(103.5000,480.8622) .. controls (103.5000,480.8622) and (82.5000,415.8622) ..
(102.0000,367.3622);
\path[xscale=0.963,yscale=1.038,fill=black,line join=miter,line cap=butt,line
width=0.800pt] (82.3229,409.0926) node[above right] (text7444) {$\sigma$};
\path[xscale=0.963,yscale=1.038,fill=black,line join=miter,line cap=butt,line
width=0.800pt] (130.4235,490.3046) node[above right] (text7448) {$\tau_1$};
\path[xscale=0.963,yscale=1.038,fill=black,line join=miter,line cap=butt,line
width=0.800pt] (181.7891,477.3222) node[above right] (text7452) {$\tau_2$};
\end{tikzpicture}
\end{document}
Finally, how. I drew over your sketch in Inkscape, then used svg2tikz to output TikZ code.
Here is my .svg file if you wish to continue with this file; you will need to fiddle slightly with the end result (e.g. arrows lose their heads)
\usetikzlibrary{tqft}
would be a good place to start