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# MathOverflow : Recent Questions and Answers (Page 3)

## Fundamental ring of a circle

Starting with fundamental group, say of a circle, let's reflect back to path groupoid a little. The path concatenation operation is partial, but this can be remedied by focusing on...

Asked on 01/01/2022 by Tegiri Nenashi

## Reference request: extendability of Lipschitz maps as a synthetic notion of curvature bounds

In the lecture Notions of Scalar Curvature - IAS around 8:00, Gromov states the following result, which he claims he does "slightly uncarefully":Suppose $(X,g_X)$ and ...

Asked on 01/01/2022 by Lawrence Mouillé

## Should cohomology of $mathbb{C} P^infty$ be a polynomial ring or a power series ring?

Some people define total cohomology of a space $X$ to be $bigoplus_{i geq 0} H^i(X)$, which would make $H^*(mathbb{C} P^infty)$ a polynomial ring in one generator of...

## Non-degenerate simplexes in a Kan complex

I have the following question on simplicial sets:a non-constant Kan complex has a non-degenerate simplex in every sufficiently large simplicial degree?It's Exercise 8.2.3 (p. 262) of Charles Weibel's book An...