espen180

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bio website location Norway age 23 member for 1 year, 10 months seen 18 hours ago profile views 142

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.

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 Aug21 answered The “Circle” is a Vector Space? Jul2 awarded Curious Jun5 accepted Degree 3 algebraic curve with a triple point Jun4 comment Degree 3 algebraic curve with a triple point That makes perfect sense! Thank you very much! Jun4 comment Degree 3 algebraic curve with a triple point @TedShifrin Do you mean that $V(f)$ is non-reduced as an affine scheme? Jun4 asked Degree 3 algebraic curve with a triple point May31 awarded Nice Answer May16 awarded Nice Question May7 comment Group representations and short exact sequences Right. But, say, semidirect products are still very difficult to handle? May7 accepted Group representations and short exact sequences May7 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? May7 answered Dimension of irreducible projective algebraic set May7 comment Proving a set is an abelian group. The last numerator should be $abc+a+b+c$, I believe. May7 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? May7 asked Group representations and short exact sequences May7 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. May7 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 $A^2=I$. May7 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 $-I$. May6 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 $\rho$. May6 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).