Chris Gerig
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 Mar 21 comment When and why is $x^x$ undefined? Check $f(-1/2)=-\sqrt{2}i$. Jan 5 awarded Yearling Dec 27 comment Augmentation ideal and the abelianization of $G$ In case it helps, an explicit isomorphism is $g[G,G]\mapsto (g-1)+I^2$. The point here is that the elements $\lbrace g-1\rbrace_{g\in G}$ form a basis for $I$ as a $\mathbb{Z}$-module, noting that $I$ is (by definition) the kernel of $\mathbb{Z}[G]\to\mathbb{Z}$ given by $g\mapsto 1$ for $g\in G$. Oct 20 comment Open in X (X is a metric space) how can you show or tell if it is open or not in general terms? What does it really mean? HINT: The typical "ball" in $[0,2]$ is NOT the same as the typical "ball" in $\mathbb{R}$ (near the value 0). Oct 16 awarded Notable Question Sep 8 comment Solutions to Dirichlet problem on manifolds with boundary And not true (for uniqueness) if $M$ is noncompact. You need a "bounded" assumption on the functions (which the Dirichlet problem typically assumes). Take $f=0$ and solutions $w_1=e^x\sin y$ and $w_2=0$ on the half-space $\lbrace(x,y)\in\mathbb{R}^2\;|\; y\ge0\rbrace$. The analytic function in the background is $e^z$. Sep 7 accepted Coupled PDE on cylinder Sep 7 asked Coupled PDE on cylinder May 21 comment is $dx$ greater than $\frac{dx}{2}$? $dx$ is not a number, so I don't know what you mean by "greater than". This is the source of your confusion, I believe. May 11 answered almost complex structures on $R^4$ Mar 20 revised Is the Pontrjagin-Thom-map null-homotopic if the normal bundle $N_i$ is trivial? wrong Thom space Mar 20 suggested approved edit on Is the Pontrjagin-Thom-map null-homotopic if the normal bundle $N_i$ is trivial? Feb 16 revised Calculating the group co-homology of the symmetric group $S_3$ with integer coefficients. deleted 331 characters in body Jan 5 awarded Yearling Dec 8 awarded Caucus Nov 11 comment Is there an interpretation of higher cohomology groups in terms of group extensions? Read Ken Brown's book Cohomology of Groups, because it explains $H^3$ as crossed-module extensions, and there is an extension-interpretation of $H^1$. In general, the higher cohomologies were described by MacLane (the appropriate references are given in this book) but are essentially intractable. Nov 9 comment Simple Branched covering over sphere. Ah you're right, I just realized I'm not answering the real question. I was only finding a complex structure such that the underlying topological surface is realized as a holomorphic cover, and as you point out, this handles all Riemann surfaces of genus 2. Nov 9 comment Simple Branched covering over sphere. Huh? The 180 degree rotation quotient map is an example of a simple branched covering for any genus, where the surface has said symmetry. Nov 8 comment Simple Branched covering over sphere. Right, and now I don't see how you can deduce anything further. You can use Riemann-Hurwitz to see that it is possible for this branched cover to have degree 2 and 2g+2 simple branch points. And we can construct this explicitly, it's given on pg105 of Donaldson (Figure 7.3), generated by 180 degree rotation. Nov 6 comment Simple Branched covering over sphere. Take a divisor of $\text{genus}+1$ points (crucial). Riemann-Roch says that the space of (nonconstant) meromorphic functions with (at worst) simple poles on the divisor is nonempty.