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seen Jun 27 at 4:01

Jul
2
awarded  Curious
Jun
4
comment Question on framed bordism classes definition
Adding to my previous comment, does this mean one can compute $\Omega_i^{fr}$ as $\Omega_{i;\mathbb{R}^k}^{fr}$ for $k\gg i$?
Jun
4
comment Question on framed bordism classes definition
Ok. That makes sense, but now I guess I have a question about stable normal bundles. Doesn't the dimension of this bundle depend on the $\mathbb{R}^n$ it is embedded into. I understand for large enough $n$ the normal bundles are all isotopic, but the normal bundle of a manifold in $\mathbb{R}^n$ is different from that when it is embedded into $\mathbb{R}^{n+1}$.
Jun
4
comment Question on framed bordism classes definition
To clarify some of my confusion, doesn't a framing require an embedding of the manifolds and a trivialization of a normal bundle, but how does this make sense for abstract manifolds?
Jun
4
revised Question on framed bordism classes definition
deleted 154 characters in body; edited title
Jun
4
asked Question on framed bordism classes definition
May
22
comment How can I prove that $Aut(C_p\times C_p)\simeq GL_2(\mathbb Z/p\mathbb Z)$?
You know that $C_p\cong \mathbb{Z}/p\mathbb{Z}$. Then given a $\phi$, look here $\phi$ takes $(1,0)$ and $(0,1)$. If you know this can you build a matrix in $GL_2(\mathbb{Z}/p\mathbb{Z})$? Do these matrices classify all the automorphism?
Apr
28
comment CW construction of a generalized lens space from Hatcher
I believe I have solved my own question. What Hatcher means by joining the $j$th edge of $C$ to $S^{2n-3}$ is to make $B^{2n-1}_j$ equal to $(z_1,\ldots,z_{n-1},z_n)$, where $z_n$ is between the $j$th and $j+1$st root of unity in $C$. In this description, it is clear the interior of this is homeomorphic to a $2n-1$ disc and the boundaries are $B_j^{2n-2}$ and $B_{j+1}^{2n-2}$.
Apr
28
comment If $|\Phi(A)|=|\Pi|$, then $O_{K}=o_{k}[A]$.
This seems to imply that $O_K$ is always generated by one element over $o_k$, which in general is not true. Am i misinterpreting something?
Apr
28
comment Limit as $x$ goes to $0$ of $x^x$
You are on the right direction. My recommendation would be to do hopital's rule in the other direction. What I mean by this is if you are considering $f(x)/g(x)$ and using Hopital's rule, try considering instead $(1/g(x))/(1/f(x))$.
Apr
28
comment Find k such that the function $f(x)=|x|^3$ is $C^{k}$ but not $C^{k+1}$
Ok. What does this mean for $f$ in relation to $C^3$? Is it in $C^3$? Is it is $C^1$ and $C^2$ (what is the derivative at $0$)?
Apr
28
comment Find k such that the function $f(x)=|x|^3$ is $C^{k}$ but not $C^{k+1}$
Try splitting up the function into positive and negative components. Ie $f(x)=x^3$ for positive $x$ and $f(x)=-x^3$ for negative $x$. When do the derivatives of these stop matching at the origin?
Apr
28
asked CW construction of a generalized lens space from Hatcher
Apr
21
comment If $|\Phi(A)|=|\Pi|$, then $O_{K}=o_{k}[A]$.
What is $L$? Is it supposed to be $K$?
Jan
22
comment Using the chain rule to prove existence of derivatives
I edited slightly. The point is that we do not know that $h'(x)$ exists, but I have seen this manipulation of symbols with the conclusion that "therefore $h'(x)$ exists".
Jan
22
revised Using the chain rule to prove existence of derivatives
added 64 characters in body
Jan
22
asked Using the chain rule to prove existence of derivatives
Jan
5
awarded  Quorum
Oct
18
awarded  Yearling
May
22
comment Question based on Triangle Inequality $\displaystyle |x+y|\leq |x|+|y|$
The lower bound can be calculated differently. Note that for $x,y,z$ at least $2$ must be on the same side of $0$, so (taking $x,y$ as this pair) $|x+y|=|x|+|y|$. Does this help?