# immersions of spheres with handles minus disks

i am at a loss as far how exactly to immerse a sphere with genus g minus a disk into the plane. Thanks in advance

• Isn't such a space just a regular neighborhood of a bouquet of circles? – Tim kinsella Dec 5 '13 at 7:39
• I am not sure, how would you get to that conclusion if you had to describe the steps? – masszz Dec 5 '13 at 7:46
• I'm not sure of the best way to see that. Do you know how to construct a genus g surface from a polygon by identifying sides? That might be one way because then you're just deleting a disc from the center of the polygon. – Tim kinsella Dec 5 '13 at 8:00
• i was thinking of using tori... i am not sure how to use your method(still wrapping my mind around these concepts) – masszz Dec 5 '13 at 8:02
• Maybe try to visualize it for a torus first. You should see how, if you make the hole wide enough, the space starts to look like two annuli stuck together (or a regular neighborhood of the wedge of two circles). For me its impossible to visualize for genus higher than that though ... – Tim kinsella Dec 5 '13 at 8:13