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| bio | website | math.berkeley.edu/~cgerig |
|---|---|---|
| location | University of California-berkeley, CA | |
| age | 24 | |
| visits | member for | 1 year, 4 months |
| seen | 16 hours ago | |
| stats | profile views | 367 |
I am an active user of MathOverflow.
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May 20 |
answered | Proving that the cohomology ring of $\mathbb{R}P^n$ is isomorphic to $\mathbb{Z}_{2}[x]/(x)^{n+1}$ |
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May 18 |
revised |
$\pi_1$ and $H_1$ of Symmetric Product of surfaces added 871 characters in body |
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May 18 |
asked | $\pi_1$ and $H_1$ of Symmetric Product of surfaces |
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May 12 |
comment |
A map on the $2n$-sphere and degree zero Let the OP do the work... |
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May 12 |
comment |
An alternative description of the first Stiefel-Whitney class This works beyond $w_1$ too. For a 4-manifold $M$ with 2nd cohomology represented by surfaces $\Sigma\subset M$, you can view $w_2(M)$ as a map $\Sigma\to \mathbb{Z}_2$ given by trivializability of $TM|_\Sigma$ (and so if this is 0 on all surfaces, then you've got a spin structure). |
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May 12 |
answered | Nontrivial h-cobordism |
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May 8 |
comment |
Tangent line of manifold No one plans to solve your homework questions for you... |
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May 6 |
awarded | Caucus |
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May 5 |
awarded | Organizer |
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May 4 |
comment |
(Elementary) applications of group (co-)homology The best place for info is Ken Brown's book Cohomology of Groups, and it will contain many applications, including the classification of low-dimensional cohomology groups in terms of group extensions. |
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May 2 |
comment |
Inducing orientations on boundary manifolds Well what will $dx(v_0)$ be in your scenario, positive or negative? And this is the same process for $k$-dimensions. |
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May 2 |
answered | Inducing orientations on boundary manifolds |
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Apr 28 |
comment |
Problem on induced maps in cohomology Then how do you get $H^n$ from $H^2$ here? Heard of naturality? |
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Apr 28 |
comment |
Problem on induced maps in cohomology Do you know the cohomology ring structure of $\mathbb{C}P^n$? |
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Apr 26 |
comment |
Canonical bundle and Möbius bundle One way, assuming you already know that there are only two real-line bundles over $S^1$, is to show that $E^\perp$ is nonorientable, or equivalently, to show that it is a nontrivial bundle by demonstrating that every section of the bundle must vanish at some point. |
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Apr 24 |
comment |
What does the group ring $\mathbb{Z}[G]$ of a finite group know about $G$? There is a difference between knowing the explicit map, and knowing the existence of the map. As soon as you posit the existence of a group ring, you have automatically posited the existence of the augmentation map! -- this is all that is needed here. Note that I cannot deduce $G_{ab}$, because I don't explicitly know the map! |
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Apr 23 |
comment |
What does the group ring $\mathbb{Z}[G]$ of a finite group know about $G$? Because I'm obviously using the augmentation map, but it doesn't matter what I use, since I'm only trying to establish the written implication. This fact is now established, and so sometime in life when you are given $\mathbb{Z}[G]=X$ and $\mathbb{Z}[H]=X$ without any other info, you can say $G_{ab}= H_{ab}$! |
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Apr 23 |
comment |
What does the group ring $\mathbb{Z}[G]$ of a finite group know about $G$? Again, this (my post) has nothing to do with your first two questions -- you asked about the implication $\mathbb{Z}[G]\cong\mathbb{Z}[H]\Rightarrow G\cong H$, to which I show you get $G_{ab}\cong H_{ab}$. |
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Apr 22 |
comment |
What does the group ring $\mathbb{Z}[G]$ of a finite group know about $G$? What doesn't work?, my proof was answering your third question. I never claimed we knew the augmentation map. |
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Apr 22 |
revised |
What does the group ring $\mathbb{Z}[G]$ of a finite group know about $G$? added 469 characters in body |
