May be this is a very silly question but it is somehow not clear to me.... If we take the space sphere with a diameter attached between north pole and south pole then if we start sliding one point towards another then we will get resulting space as circle inside the sphere attach at one point (let say north pole). Now how to see that this space is homotopy equivalent to wedge sum of Sphere and circle(here circle is outside the sphere ).Now what is not clear to me is how to take that circle out from inside to outside??
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You have the diameter attached and then you identify south and north-pole? Or you just identify all the diameter to one point? – Peter Franek Jul 13 '16 at 07:30
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2If you increase the dimensions where you embed your initial sphere with a diameter ... then in the final step you can easily take out the circle from the inside of sphere without intersecting sphere... For example dimension 4 is enough for see this – Anubhav Mukherjee Jul 13 '16 at 07:34
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@anubhav sorry this is not clear to me...can you please elaborate or you can give the homotopy... – Shivani Sengupta Jul 13 '16 at 08:42