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Spivak on 1-cubes

  1. Aug 17, 2005 #1
    I think I'm missing something in his description. Spivak defines a singular k-cube as a continuous function from the solid paralleletope [0,1]k into a subset of Rn. He also defines the singular 1-cube cR,n:[0,1] -> R2-{0}:t |-> (R cos((2Pi) n t), R sin((2Pi) n t)).
    So in one exercise, we have a singular 1-cube c in R2-{0} where c(0)=c(1), and we are asked to show that there is an integer n such that c-c1,n is the boundary of some sum of 2-cubes. He later asks to show that n is unique.
    Now, c1,n is just the unit circle wound around the origin n times. I don't see the difference between c1,1 and c1,2 with respect to bounding 2-dimensional regions. What is the right way to look at this ?
  2. jcsd
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