999 reputation
521
bio website math.berkeley.edu/~cgerig
location UC Berkeley
age 26
visits member for 3 years
seen 3 hours ago

After doing my BS in engineering physics, I started my PhD in experimental atomic physics. But I quit to do math, and am now a student of Michael Hutchings!


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.
Oct
21
revised Determining an explicit line bundle over surface
added 24 characters in body
Oct
5
revised Determining an explicit line bundle over surface
edited title
Oct
4
revised Determining an explicit line bundle over surface
deleted 497 characters in body; edited title
Oct
3
revised Determining an explicit line bundle over surface
added 19 characters in body
Oct
2
asked Determining an explicit line bundle over surface
Sep
13
answered A smooth function $f:S^1\times S^1\to \mathbb R$ must have more than two critical points.
Aug
19
awarded  Necromancer
Aug
4
answered Cup product in Morse cohomology
Jul
30
answered Non-ellipticity of Yang-Mills equations
Jul
22
comment Are distance-related paradoxes limited by the size of an atom?
This isn't math... this is philosophy.
Jul
2
awarded  Curious
May
29
comment Is there a “standard” way to compute the fundamental group of the $CP^n$?
math.stackexchange.com/questions/589134/…
Apr
27
comment Determinants Problem
We are not here to do computations for you. Show your work and where you are stuck. In particular, do you not know how to compute a determinant?