Amitesh Datta
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 Apr 1 awarded Electorate Sep 9 awarded Fanatic Sep 6 awarded Notable Question Aug 26 awarded Good Question Aug 12 comment Intuition behind the following theorem of Reeb? A Morse function on a smooth manifold $M$ gives rise to a handlebody decomposition of $M$, with an $i$-handle for each index $i$ critical point. In the case of Reeb's theorem, there is one index $0$ critical point (minimum) and one index $n$ critical point (maximum), and so $M$ is obtained by attaching an $n$-handle to a $0$-handle, i.e., gluing two $n$-balls by identifying their boundary $\mathbb{S}^{n-1}$'s. However, this is simply $\mathbb{S}^n$ (Alexander's trick). May 26 comment What's the name of this branched covering? Dear @paul, thank you for your comment! :) I guess in that case one can also state that the genus of the surface will be the ceiling of $\frac{\text{deg}(f)-2}{2}$. May 25 comment What's the name of this branched covering? Hi @Balarka, is that true? For example, you can exhibit any Riemann surface as a branched double cover of $\mathbb{CP}^1$ (to exhibit this geometrically, put a skewer symmetrically through the surface and let $\mathbb{Z}/2$ act as rotation by 180 degrees about the skewer). May 22 awarded Famous Question Mar 29 comment What is the $L^p$-norm of the (uncentered) Hardy-Littlewood maximal function? Thank you so much for your answer, Mark! (I'm very sorry I didn't see it until now.) I really, really appreciate that you took the time to write such a detailed answer. Thank you! Mar 29 accepted What is the $L^p$-norm of the (uncentered) Hardy-Littlewood maximal function? Mar 28 awarded Enthusiast Mar 23 awarded Yearling Dec 23 awarded Autobiographer Nov 29 awarded Favorite Question Jul 2 awarded Curious Mar 20 awarded Popular Question Feb 17 awarded Necromancer Jan 24 awarded Popular Question Sep 30 awarded Caucus Sep 2 awarded Civic Duty