Reputation
10,129
Next privilege 15,000 Rep.
Protect questions
Badges
26 45
Impact
~140k people reached

Nov
18
comment Complex structure on a real vector bundle
$J$ is the complex structure. The $e_i$ and $\sigma_i$ are local sections of $E$ and so are acted on by $J$. Having a trivialization (i.e. iso from $E$ restricted to $U$ to $U\times \mathbb R^{2n}$) is equivalent to having $2n$ pointwise independent sections of $E$ restricted to $U$.
Nov
18
answered Complex structure on a real vector bundle
Nov
17
comment Complex structure on a real vector bundle
Are you familiar with how a metric on a vector bundle reduces the structure group to the orthogonal group?
Oct
27
comment Lie Bracket, Hopf Fibration, independence of choice
A horizontal lift is not unique unless you fix a connection on the fibration.
Oct
20
awarded  Notable Question
Sep
24
awarded  Autobiographer
Aug
25
awarded  Enlightened
Aug
25
awarded  Nice Answer
Aug
22
answered Definite Integral theorem validity :- $\int_{0}^{L} \left( \int_{s}^{L}p(t)\ dt \right) \ ds =\int_{0}^{L} \ p(s) \ ds$?
Aug
14
comment Is this a manifold?
So you're looking at the sphere with like a ring around it thats touching it? This won't be locally homeomorphic to $\mathbb R^2$.
Jul
26
revised Complex structures on Riemann surfaces
added 171 characters in body
Jul
25
comment Homeomorphism between SU(4) and SO(6)
The maps $SU(2) \to SO(3)$ and $SU(4) \to SO(6)$ are not homeomorphisms but are 2-to-1 Lie group covering maps (so local homeomorphisms).
Jul
24
revised Complex structures on Riemann surfaces
edited tags
Jul
24
asked Complex structures on Riemann surfaces
Jul
24
comment Submersions and induced homomorphism on fundamental groups
I think you need a little more justification for the existence of the $\alpha_i$. You could use for example the regular value theorem (which maybe you implicitly are).
Jul
20
awarded  Yearling
Jul
12
awarded  Good Question
Jul
8
awarded  Popular Question
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive