mjhjmtu

How do we draw a figure like this in tikz?

I am able to draw the straight lines, but these curves are too challenging -- how to draw them nice?

The minimal template is:

begintikzpicture
draw[->] (0,0,0)--(0,8,0);
draw[->] (4,0,0)--(4,8,0);
endtikzpicture

I really appreciate your patience!

That's a standard task for the knot library.

documentclass[tikz,border=3.14mm]standalone
usetikzlibraryknots,arrows.meta
begindocument
begintikzpicture
path (-0.5,6.5) coordinate (x1) (4.5,5) coordinate (x2) 
(-0.5,3.5) coordinate (x3) (4.5,2.5) coordinate (x4); 
beginknot%[draft mode=crossings]
strand[Circle-Circle] (0,0) -- (0,8);
strand[Circle-Circle] (4,0) -- (4,8);
strand[Circle-Circle,looseness=0.5] (2,8) to[out=-90,in=90] (x1)
to[out=-90,in=90] (x2) to[out=-90,in=90] (x3)
to[out=-90,in=90] (x4) to[out=-90,in=90] (2,0);
flipcrossings2,4,6,8
endknot
endtikzpicture
enddocument

Or with the ordering as in your picture.

documentclass[tikz,border=3.14mm]standalone
usetikzlibraryknots,arrows.meta
begindocument
begintikzpicture
path (-0.5,6.5) coordinate (x1) (4.5,5) coordinate (x2) 
(-0.5,3.5) coordinate (x3) (4.5,2.5) coordinate (x4); 
beginknot%[draft mode=crossings]
strand[Circle-Circle] (0,0) -- (0,8);
strand[Circle-Circle] (4,0) -- (4,8);
strand[Circle-Circle,looseness=0.5] (2,8) to[out=-90,in=90] (x1)
to[out=-90,in=90] (x2) to[out=-90,in=90] (x3)
to[out=-90,in=90] (x4) to[out=-90,in=90] (2,0);
flipcrossings2,3,5,8
endknot
endtikzpicture
enddocument

To find out which crossing has which number, uncomment [draft mode=crossings].

Here's a version in plain Metapost featuring a useful idiom to find all the intersection points between two paths.

This is wrapped up in luamplib so compile it with lualatex (or work out how to adapt it for plain mpost).

documentclass[border=5mm]standalone
usepackageluatex85
usepackageluamplib
begindocument
mplibtextextlabelenable
beginmplibcode
beginfig(1);
 path s, t, a, b;
 a = (down--up) scaled 164 shifted 72 left;
 b = (down--up) scaled 164 shifted 72 right;
 t = ((-36*4, 0) for x=-35 upto 36: .. (4x, 88 sind(10x)) endfor) rotated 90 reflectedabout(up, down);
 s = point 0 of t shifted 20 down up .. direction 2 of t subpath (2,70) of t direction 70 of t .. point 72 of t shifted 20 up up;

 pickup pencircle scaled 1;

 forsuffixes $=a, b, s:
 draw $;
 fill fullcircle scaled 4 shifted point 0 of $;
 fill fullcircle scaled 4 shifted point infinity of $;
 endfor

 vardef over_and_under(expr a, b) = 
 save x, y, r, n, A, B, p;
 path r; numeric n; picture A, B, p;
 r := a;
 n = 0;
 forever:
 r := r cutbefore b;
 exitif length cuttings = 0;
 r := subpath (epsilon, infinity) of r;
 z[incr n] = point 0 of r;
 endfor
 A = image(draw a);
 B = image(draw b);
 for i=0 upto n:
 if known z[i]:
 unfill fullcircle scaled 10 shifted z[i];
 p := if odd i: B else: A fi;
 clip p to fullcircle scaled 10 shifted z[i];
 draw p;
 fi
 endfor
 enddef;

 over_and_under(a, s);
 over_and_under(b, s);

endfig;
endmplibcode
enddocument

Here is an attempt using the snake decoration from tikz library decorations.pathmorphing. The intersections library is used to calculate the crossovers locations. White circles are then drawn at intersection points.

documentclass[tikz,border=5pt]standalone
usetikzlibraryintersections,decorations.pathmorphing
begindocument

begintikzpicture[thick,rotate=90,xscale=.7,dot/.style=inner sep=1.5pt,fill,circle,cut/.style=inner sep=3pt,fill=white,circle]

draw[name path=curve,decorate, decoration=snake, segment length=2.96cm, amplitude=-2cm] (0,0)node[dot] -- (9,0)node[dot];
path[name path=la](-1, 1.5) -- (10, 1.5);
path[name path=lb](-1,-1.5) -- (10,-1.5);

path [name intersections=of=la and curve];
node[cut] at(intersection-1) (intersection-4) node[cut] (intersection-2) node(2)[cut,fill=none] (intersection-3) node(3)[cut,fill=none];
draw (-1,1.5) node[dot] -- (2) (2) -- (3) (3) -- (10,1.5) node[dot];

path [name intersections=of=lb and curve];
node[cut] at(intersection-2) (intersection-3) node[cut] (intersection-1) node(1)[cut,fill=none] (intersection-4) node(4)[cut,fill=none];
draw (-1,-1.5) node[dot] -- (1) (1) -- (4) (4) -- (10,-1.5) node[dot];

endtikzpicture

enddocument