u/Material-Way8007

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.