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 Yearling
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Jan
27
comment Examples of Lattices in $\operatorname{Isom}(H^n)$ for all $n \geq 2$?
Interesting idea. Certainly such surfaces do not exist if they can be embedded in $\mathbb{R}^{3}$ (it's a standard differential geometry proof to show that there must exist a point for which the sectional curvature is strictly positive). This MathOverflow post suggests that it is possible that one can create such manifolds, but it's certainly not something I would have come up with during an exam: mathoverflow.net/questions/32597/…
Jan
27
answered Interior of the Graph of $\sin(1/x)$
Jan
27
asked Examples of Lattices in $\operatorname{Isom}(H^n)$ for all $n \geq 2$?
Jan
27
comment Interior of the Graph of $\sin(1/x)$
Are you considering the graph of $\sin(1/x)$ as a subset of $\mathbb{R}^{2}$?
Jan
1
accepted Discrete group of isometries of a finitely compact metric space is countable.
Jan
1
comment Discrete group of isometries of a finitely compact metric space is countable.
Oh ok, that makes it perfectly clear now. Thanks!
Jan
1
awarded  Yearling
Jan
1
comment Find the matrix inverse
For part (a), notice that $A-B^{-1} = (AB-I)B^{-1}$, so $(A-B^{-1})^{-1}=B(AB-I)^{-1}$. Part (b) should have a similar approach - find a way to represent that matrix as a product of invertible matrices that you do know.
Jan
1
comment Discrete group of isometries of a finitely compact metric space is countable.
I think I see the finiteness of $\Gamma p \cap B(p,n)$ (since the orbit is discrete), but I'm not totally sure how it finishes the proof. Are you suggesting somehow that we can get a base for the topology using open balls of various radii centered at the points in the orbit $\Gamma p$?
Dec
31
asked Discrete group of isometries of a finitely compact metric space is countable.
Sep
29
awarded  Popular Question
Mar
26
comment Help with old exam question relating a spanning set of covectors of $T_{p}^{*} M$ to a coordinate chart containing $p$.
Doh! That makes perfect sense and is so much cleaner than what I was trying to do. Thank you very much.
Mar
26
accepted Help with old exam question relating a spanning set of covectors of $T_{p}^{*} M$ to a coordinate chart containing $p$.
Mar
26
asked Help with old exam question relating a spanning set of covectors of $T_{p}^{*} M$ to a coordinate chart containing $p$.
Dec
11
awarded  Caucus
Nov
29
asked Counting tamely ramified Galois extensions of $\mathbb{Q}_p$ with a given Galois group.
Aug
18
comment If G is a group of order n=35, then it is cyclic
As others have said, this proof does not work because you don't know <i>a priori</i> that it is abelian. It's entirely possible that $gh$ has infinite order (see: above matrix example). Let $n_p$ denote the number of Sylow $p$-subgroups of $G$. We know that $n_p \equiv 1 \pmod p$ and $n_p \mid 35$. We deduce from this that $n_5 = n_7 = 1$, so both the $5$-subgroup, $C_5$, and $7$-subgroup, $C_7$, are normal in $G$. By normality, we have that $C_5 C_7 < G$. Moreover, since $C_5 \cap C_7 = \{1\}$, $C_5 C_7 = C_5 \times C_7 \cong C_{35}$, and finiteness of $G$ implies that $G = C_{35}$.
Jul
2
awarded  Curious
Apr
30
accepted Help Understanding/Completing Proof of Prop 3.18/3.19 in Hatcher's Algebraic Topology
Apr
30
answered Help Understanding/Completing Proof of Prop 3.18/3.19 in Hatcher's Algebraic Topology