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There are informative and easily accessible images and videos that illustrate the Hopf fibration $S^3\to S^2$ by describing what happens to the fibers in the unit cube $(0,1)^3\approx S^3\backslash \...

I know this is just $S^2$. To see it, I use the CW structure of $S^1$ x $S^1$ , consisting of one 0-cell, two 1-cells and a 2-cell. Then since the reduced suspension is the cartesian product ...

The shortest form of this question is: How much TDA can be done with tSNE? Specifically, I'm referring to the application of TDA to clustering data, so, think along the lines of Ayasdi's ...