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Feb 16, 2018 at 17:26 comment added Jānis Lazovskis Yes, as that is the closest thing I could think of of related to your question.
Feb 14, 2018 at 19:00 comment added Ryan Budney @JānisLazovskis: It sounds like you are referring to the codimension zero strata? There are also tangencies and triple point avoidance.
Feb 11, 2018 at 15:35 comment added Jānis Lazovskis The $v_i$ are not quite the configuration space $\text{Conf}_n(\mathbf{R}^2)$ because you are allowing circles to coincide, but also not quite the Ran space $\text{Ran}^{\leqslant n}(\mathbf{R}^2)$, because you are keeping track of how many points coincide (and their order). Ayala-Francis-Tanaka (Example 3.5.17 and onwards) write about how $X^I$, for $I$ finite, sits in an already stratified Ran space, which may give you some coarser information.
Feb 10, 2018 at 22:50 history asked Ryan Budney CC BY-SA 3.0