college math

posted by .

The classification of closed orientable surfaces says that they are all spheres with a certain number of handles attached. For example, a sphere is a sphere with 0 handles. A torus is a sphere with one handle. A two holed torus is a sphere with two handles etc. How does one "attach a handle"? Think of puncturing a surface as "removing a lid". After all if you make a puncture, you can stretch out the hole into a square shape which you can think of as being the ghost of a panel in the construction of the original surface. So the puncture is removing a lid. What does "removing a lid" do to the Euler characteristic and number of boundary curves?

  • college math -

    Hey, ML, why didn't you use Y@hoo! Answers like everyone else in Finston's math class? Are those even your real initials? Mysterious. He tells you how to attach a handle in the next bullet point. Removing a lid does nothing to the Euler characteristic but increases the number of boundary curves. I could be wrong after all I don't really pay attention. See you next Monday.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics/chem

    n Fig. 21-41, three identical conducting spheres initially have the following charges: sphere A, 7Q; sphere B, -8Q; and sphere C, 0. Spheres A and B are fixed in place, with a center-to-center separation that is much larger than the …
  2. college physics

    Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B?
  3. college physics

    Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B?
  4. physics

    consider three identical metal spheres a b and c. sphere a carries a charge of +5q. sphere b carries a charge of -q. sphere c carries no net charge. spheres a and b are touched together and then separated. sphere c is touched to sphere …
  5. College Physics II

    Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters. The electrostatic force acting on sphere 2 due to sphere 1 is F. Suppose now that a third …
  6. science

    two equally charged spheres, X and Y, repel each other with a force of 8.0 x 10^-6 N when placed a certain distance apart. Another identical, but uncharged, sphere is touched to sphere Y and then moved next to sphere X. Calculate the …
  7. Physics

    Three identical conducting spheres initially have the following charges: sphere A, 4Q; sphere B, -9Q; and sphere C, 0. Spheres A and B are fixed in place, with a center-to-center separation that is much larger than the spheres. Two …
  8. math

    The classification of closed orientable surfaces says that they are all spheres with a certain number of handles attached. For example, a sphere is a sphere with 0 handles. A torus is a sphere with one handle. A two holed torus is …
  9. Urgent : Electricity and Magnetism

    Two charged spheres are kept at a great distance from each other. Sphere A has charge +20q and sphere B has charge -14q. A neutral conducting sphere, sphere X, is then touched upon the sphere A, then sphere B, and X, repectively, after …
  10. Shegal

    Three identical metal spheres are hung from a ceiling on rigid non-conducting rods. Sphere 1, sphere 2, and sphere 3 have charges 75 µC, −44 µC, and 50 µC, respectively. Each sphere is separated by 0.15 m. What is the net …

More Similar Questions