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](adsbygoogle = window.adsbygoogle || []).push({}); ^{k}into a subset of R^{n}. He also defines the singular 1-cubec:[0,1] -> R_{R,n}^{2}-{0}:t |-> (R cos((2Pi) n t), R sin((2Pi) n t)).

So in one exercise, we have a singular 1-cubecin R^{2}-{0} where c(0)=c(1), and we are asked to show that there is an integernsuch thatc-cis the boundary of some sum of 2-cubes. He later asks to show that_{1,n}nis unique.

Now, c_{1,n}is just the unit circle wound around the origin n times. I don't see the difference between c_{1,1}and c_{1,2}with respect to bounding 2-dimensional regions. What is the right way to look at this ?

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# Spivak on 1-cubes

Can you offer guidance or do you also need help?

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