Daan Michiels
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 Dec14 awarded Yearling Oct23 comment If the absolute value of a function is continuous, is the function continuous? I assumed the domain was the integers because the way I see it, a number $x$ has to be an integer for the statement '$x$ is odd' to make sense. I guess that's a matter of convention, though. The wording 'if $x$ is an odd integer', plus an indication of what the domain is, would make the answer clearer. Oct5 comment If the absolute value of a function is continuous, is the function continuous? This function is continuous. (I assume its domain is the integers?) Jul2 awarded Curious Jun16 comment Natural connection on tautological bundle over real Grassmannian Thanks, that makes a lot of sense. Let me summarize how parallel transport works in my own words. Let $W(t)$ be a path in $G(k,V)$ and $w\in W(0)$ (so that the pair $(w,W(0))$ is in the tautological bundle). There is a unique path $w(t)$ in $V$ such that $w(t)\in W(t)$ and $w'(t) \perp W(t)$ for all $t$. Parallel transport of $(w,W(0))$ along $W(t)$ is $(w(t),W(t))$. Jun16 accepted Natural connection on tautological bundle over real Grassmannian Jun12 comment Prove that $|x - y| \geq |x| - |y|$ As a general strategy for finding where your mistake is, plug in some easy numbers. Jun12 answered Prove that $|x - y| \geq |x| - |y|$ Jun12 asked Natural connection on tautological bundle over real Grassmannian Apr10 comment explicit cocycle representing Stiefel-Whitney class in Milnor and Stasheff In problem 6-C you only have an embedding of $G_n(\mathbb{R}^m)$ into $G_{n+1}(\mathbb{R}^{m+1})$, and which sends $r$-cells to $r$-cells. However, I think that not all $r$-cells have to be in the image of this embedding (as can be seen by counting $r$-cells). In particular, the induced map in cohomology $H^r(G_{n+1}(\mathbb{R}^{m+1})) \to H^r(G_{n}(\mathbb{R}^{m}))$ is not injective. Therefore, you cannot deduce the Stiefel-Whitney class in $H^r(G_{n+1}(\mathbb{R}^{m+1}))$ from the one in $H^r(G_{n}(\mathbb{R}^{m}))$. Or at least, I don't see how. Mar13 comment Under what conditions the quotient space of a manifold is a manifold? This is in fact equivalent to $M/E$ having a smooth structure compatible with the quotient topology such that $M\to M/E$ is a submersion, according to math.illinois.edu/~ruiloja/Math519/notes.pdf, theorem 8.3 on page 63. (if by submanifold you mean embedded submanifold) Mar2 reviewed No Action Needed Under what conditions are trigonometric integrals over a period zero? Dec14 awarded Yearling Oct28 awarded Self-Learner May22 accepted Every principal $G$-bundle over a surface is trivial if $G$ is compact and simply connected: reference? May16 comment Every principal $G$-bundle over a surface is trivial if $G$ is compact and simply connected: reference? Thanks for the answer. Any reference I can take a look at? May15 answered Deduce dice configuration knowing 2 adjacent faces May14 comment The number of words that can be made by permuting the letters of _MATHEMATICS_ is Example: the number of words that can be made by permuting the letters of BEER is 12. The possibilities are EEBR, EERB, EBER, EREB, EBRE, ERBE, BERE, REBE, BREE, RBEE, BEER, REEB. May14 awarded Caucus Apr25 comment Every principal $G$-bundle over a surface is trivial if $G$ is compact and simply connected: reference? @EricO.Korman - Thank you, that helps (though I have to think about it a little bit).