/sci/ - Science & Math

>>11696424
Then you don't mention them. Keep them hidden, keep your mouth shut, only speak of them if you are asked.

>>11696428
Remove a point from the Euclidean plane to get a space homotopy equivalent with the unit circle. Do the same for the complex plane and a neighbourhood of a fixed point containing no other fixed points. Restricting to the boundary of that nbd, you get a map from to the unit circle, and then you just count how many full laps you make and in which direction. Excluding Lefschetz, I can't think of many uses for this. I guess you could use it to distinguish between different maps sharing a fixed point if they have different indices, or if the index is 0 then you don't go around the circle (and thus your map g is null homotopic). Can you make any conclusions out of these?