161,305 reputation
16351646
bio website math.berkeley.edu/~qchu
location Berkeley, CA
age 24
visits member for 4 years, 6 months
seen 2 hours ago

I am a third-year graduate student at UC Berkeley. I'm interested in the interplay between homotopy theory, quantum field theory, manifold topology, and higher category theory.


3h
comment Is there an established method for assigning a truth value $0<t<1$ to undecidable statements?
Me too, but you didn't specify what kind of intermediate truth values you were looking for.
3h
comment Homology group $H_1(G;\mathbb{R})$ is a vector space?
@user1729: for one thing, it can be finite-dimensional even if $G$ is infinite. Note also that your construction makes no use of the group structure of $G$. And yes.
12h
comment If a set $\Sigma$ of alphabets is of cardinality $k$, does $\Sigma^n$ have cardinality of $k^n$?
Yes. That's what the notation is suggesting.
13h
comment Is reduced homology a full functor on connected spaces?
@k.stm: a rough summary is that in some special cases you can actually compute the homotopy classes of maps between two spaces and just check that there aren't enough of them to induce all maps between their homologies. Although there is this subtlety about endomorphisms vs. automorphisms.
13h
comment How to calculate $\exp(-x)$ using Taylor series
Oog. Why not start the summation at $0$?
13h
revised Is reduced homology a full functor on connected spaces?
Edited so I can remove a downvote.
15h
comment Mipoint between points in projective space
Think of $\mathbb{P}^1$ as the $2$-sphere $S^2$, and pick two antipodal points. What could their midpoint possibly be?
16h
comment Eigenvalues of operator on $S_n$'s group algebra
Certainly they should have large multiplicities, but that doesn't mean they have to be nice. If you know the eigenvalues of your sum acting on each irreducible representation $V$ of $S_n$, then you know the eigenvalues of it acting on the group algebra: for each $V$, it's $|\dim V|$ copies of the eigenvalues acting on $V$. But you still have to know something about how your sum acts on each irreducible representation $V$. A lot is known about the irreducible representations of $S_n$ but it's probably a painful and unenlightening mess to extract what you want from that information.
22h
comment Is reduced homology a full functor on connected spaces?
Oh, interesting. Sorry for the downvote, then; I can't remove it anymore.
23h
answered Homology group $H_1(G;\mathbb{R})$ is a vector space?
23h
comment Is reduced homology a full functor on connected spaces?
It means that "yes" and "no" become ambiguous. It's not a big deal, it's just slightly annoying.
1d
comment Is reduced homology a full functor on connected spaces?
For a simpler example, there are maps of rings which are surjective but which aren't surjective on groups of units, such as $\mathbb{Z} \to \mathbb{Z}_5$.
1d
comment Is reduced homology a full functor on connected spaces?
I don't think this answers the question. You're showing that homology isn't surjective on isomorphisms, which does not imply that it isn't full.
1d
revised Is reduced homology a full functor on connected spaces?
added 320 characters in body
1d
comment Is reduced homology a full functor on connected spaces?
+1 for asking the same question in the title and the body! (Some people have a habit of asking "Q?" in the title and "not-Q?"in the body.)
1d
answered Is reduced homology a full functor on connected spaces?
1d
answered Is there an established method for assigning a truth value $0<t<1$ to undecidable statements?
1d
comment Non-trivial characters of $SU(2)$
There are lots of things you could do depending on your level of sophistication. You could try to show explicitly that $SU(2)$ has trivial abelianization by writing every element as a product of commutators. Or you could use any number of methods to more generally classify the irreducible representations of $SU(2)$ (this is classical and important) and check that there's only one $1$-dimensional irrep.
1d
comment Non-trivial characters of $SU(2)$
By a character do you mean a homomorphism to $\mathbb{C}^{\times}$? If so, then no.
1d
answered Basic sanity check: dimension of Lie groups / tangent spaces