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## Main Question or Discussion Point

I've been doing a project on Henri Poincare and I am attempting to explain his conjecture to my Calculus class so I am using the common lower dimensional equivalent to do so. If a rubber band is wrapped around an object and becomes smaller and smaller until it is a point than that object is homeomorphic to a sphere and contrast this with the case of a torus.

My problem is that I am confused as to whether the Poincare conjecture involves wrapping a one dimensional line around a four dimensional figure or if it is a two dimensional plane around a four dimensional figure. I am only briefly mentioning this so the answer shouldn't be too complex.

My problem is that I am confused as to whether the Poincare conjecture involves wrapping a one dimensional line around a four dimensional figure or if it is a two dimensional plane around a four dimensional figure. I am only briefly mentioning this so the answer shouldn't be too complex.