Surfaces¶
Bigger comes with a number of premade surfaces.
These available within bigger.load
Flute¶

bigger.load.
flute
() → bigger.mappingclassgroup.MappingClassGroup[int][int][source]¶ The infinitely punctured sphere, with punctures that accumulate in one direction.
With mapping classes:
 a_n which twists about the curve parallel to edges n and n+1
 b_n which twists about the curve which separates punctures n and n+1
 a{expr(n)} which twists about all a_n curves when expr(n) is True
 b{expr(n)} which twists about all b_n curves when expr(n) is True
Shortcuts:
 a[start:stop:step] = a{n in range(start, stop, step)}
 a == a[:]
Biflute¶

bigger.load.
biflute
() → bigger.mappingclassgroup.MappingClassGroup[int][int][source]¶ The infinitely punctured sphere, with punctures that accumulate in two directions.
With mapping classes:
 a_n which twists about the curve parallel to edges n and n+1
 b_n which twists about the curve which separates punctures n and n+1
 a{expr(n)} which twists about all a_n curves when expr(n) is True
 b{expr(n)} which twists about all b_n curves when expr(n) is True
 s which shifts the surface down
 r which rotates the surface fixing the curve a_0
Shortcuts:
 a[start:stop:step] = a{n in range(start, stop, step)}
 a == a[:]
Note: Since b_n and b_{n+1} intersect, any b expression cannot be true for consecutive values.
Cantor¶
Spotted Cantor¶

bigger.load.
spotted_cantor
() → bigger.mappingclassgroup.MappingClassGroup[typing.Tuple[int, int]][Tuple[int, int]][source]¶ The uncountablypunctured sphere.
With mapping classes:
 a_n which twists about the curve across square n
 a{expr(n)} which twists about all a_n curves when expr(n) is True
Shortcuts:
 a[start:stop:step] = a{n in range(start, stop, step)}
 a == a[:]
Loch Ness Monster¶

bigger.load.
loch_ness_monster
() → bigger.mappingclassgroup.MappingClassGroup[int][int][source]¶ The infinitegenus, oneended surface.
With mapping classes:
 a which twists about the longitudes of the monster
 b which twists about the meridians of the monster
 c which twists about the curves linking the nth and n+1st handles
 s which shifts the surface down
Ladder¶
Spotted Ladder¶

bigger.load.
spotted_ladder
() → bigger.mappingclassgroup.MappingClassGroup[typing.Tuple[int, int]][Tuple[int, int]][source]¶ The infinitegenus, twoended surface.
With mapping classes:
 a_n which twists about the curve parallel to edges n and n+1
 b_n which twists about the curve which separates punctures n and n+1
 a which twists about all a_n curves simultaneously
 b which twists about all b_n curves simultaneously
 s which shifts the surface down