1,882 reputation
213
bio website
location Norway
age 23
visits member for 1 year, 10 months
seen 18 hours ago

I'm a 1st year master's student of mathematics, specializing in algebraic topology.

I have Bc.S. degrees in mathematics and physics.

My interests include topology, geometry and mathematical physics, and more specifically abstract homotopy theory and cobordism theory.


Aug
21
answered The “Circle” is a Vector Space?
Jul
2
awarded  Curious
Jun
5
accepted Degree 3 algebraic curve with a triple point
Jun
4
comment Degree 3 algebraic curve with a triple point
That makes perfect sense! Thank you very much!
Jun
4
comment Degree 3 algebraic curve with a triple point
@TedShifrin Do you mean that $V(f)$ is non-reduced as an affine scheme?
Jun
4
asked Degree 3 algebraic curve with a triple point
May
31
awarded  Nice Answer
May
16
awarded  Nice Question
May
7
comment Group representations and short exact sequences
Right. But, say, semidirect products are still very difficult to handle?
May
7
accepted Group representations and short exact sequences
May
7
comment Group representations and short exact sequences
Thank you very much. I assume it is safe to assume that the characteristic zero, even algebraically closed case is not any simpler?
May
7
answered Dimension of irreducible projective algebraic set
May
7
comment Proving a set is an abelian group.
The last numerator should be $abc+a+b+c$, I believe.
May
7
comment Group representations and short exact sequences
You have the inclusion $SO(n)\rightarrow O(n)$, which is the kernel of the determinant $O(n)\rightarrow \mathbb{Z}_2$. The first map is injective, the last one is surjective, so it is an exact sequence. What is the map $O(n)\rightarrow SO(n)$ you had in mind?
May
7
asked Group representations and short exact sequences
May
7
comment Can we regard Hausdorff space as a manifold?
Minor correction/comment: If your definition of manifold includes paracompactness, then every manifold is a metric space.
May
7
comment Relationship between O(n)- and SO(n)-representations?
For odd $n$, $-I$ has determinant $-1$. Since $-I$ is a (the only nontrivial) central element in $O(n)$, this gives a nice isomorphism between $O(n)$ and $SO(n)\times Z_2$. In the case of even $n$, the best you can do is that $O(n)$ is isomorphic to a semidirect product $SO(n)\rtimes G$, where $G=\{I,A\}$ for some orthogonal matrix $A$ for which $det(A)=-1$ and $A^2=I$.
May
7
comment Relationship between O(n)- and SO(n)-representations?
At least for odd $n$, I imagine it is sufficient to look at the action of $-I$.
May
6
comment Definition of a lift in algebraic topology
Yes, then by definition, $\tilde{f}$ is a lift of $f$ through $\rho$. Of course, we rarely want just any lift, but one through a specified map $\rho$.
May
6
comment Definition of a lift in algebraic topology
Not at all, we can ask this question for any $\tilde{X}$ and $\rho$ whatsoever. However, in many naturally occurring situations, $\rho$ does have properties resembling a covering space (specifically, it is often a fibration).