This is just some facebook engagement slop i found, but isn’t the correct answer to this 7? Because if i imagine it being infinitely flexible, i open it up from the body hole, and lay it flat with the headhole in the middle. There is the head hole, 2 arm holes, and 4 cut holes, right?
Are there open problems in topology that are appropriate for an undergraduate to solve over the summer? I've taken a the year-long graduate course in algebraic topology which covered roughly the following topics: fundamental group, covering spaces, (co)homology with coefficients, cup/cap products + Poincare duality, higher homotopy groups, fiber bundles/fibrations. I'm planning on reading Milnor and Stasheff's book on characteristic classes over the summer and will be writing a senior thesis on topological K-theory next year.