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May
7
awarded  Enlightened
May
7
awarded  Nice Answer
May
5
comment String Theory: What to do?
@user02138: but isn't there more interesting math related to string theory (e.g. algebraic geometry, mirror symmetry) than qft? I know of mathematicians working in math related to string theory but don't know of any working in math related directly to qft.
May
5
comment rescaled metric quantities on rescaling metrics
@unk2: $S_{g_1} = \frac{1}{a} S_g$.
May
5
answered rescaled metric quantities on rescaling metrics
May
3
comment Can one use Atiyah-Singer to prove that the Chern-Weil definition of Chern classes are $\mathbb{Z}$-cohomology classes?
@Aaron: Do you have a link to the analytic proof?
May
2
answered every map can be replaced by a weakly equivalent fibration
May
2
comment Showing a hypersurface is contained in a level set of a regular value
@user8268: thanks!
May
2
comment Can one use Atiyah-Singer to prove that the Chern-Weil definition of Chern classes are $\mathbb{Z}$-cohomology classes?
If you accept the proof that Chern classes are characterized by the naturality, sum formula, and normalization axioms, then doesn't it follow that the Chern-Weil definition must lie in $\mathbb Z$-cohomology? But anyways, I am interested in an answer to this question.
Apr
26
awarded  Good Question
Apr
24
revised Classification of general fibre bundles
added 21 characters in body
Apr
24
comment Classification of general fibre bundles
@Matt: in the rank $k$ vector bundle case the base space is the Grassmannian of $k$-planes in $\mathbb R^\infty$. Does this really generalize in the proof you saw to give the base space when the fiber is arbitrary?
Apr
24
comment Classification of general fibre bundles
I should have mentioned in my question that I know what I said holds true for $G$ a Lie group. But does this still hold if $G$ is any topological group? Also, if $F$ is a CW complex is $Aut(F)$ also?
Apr
24
asked Classification of general fibre bundles
Apr
21
comment Showing a hypersurface is contained in a level set of a regular value
Say $H(S) = c$. Then in general $H^{-1}(c)$ will have to contain more than $S$. How can I guarantee other points in $H^{-1}(c)$ are not critical?
Apr
21
comment Showing a hypersurface is contained in a level set of a regular value
@user8268: It looks like in your construction $S = H^{-1}(0)$? That can't work in general.
Apr
21
comment Showing a hypersurface is contained in a level set of a regular value
@user8268: Can you be more specific? If I simply extend the map by multiplying by a bump function then 0 will no longer be a regular value.
Apr
21
comment Showing a hypersurface is contained in a level set of a regular value
Do you really mean composition? $pr_2$ is not defined on all of $M$, only on an open set. If I multiply $pr_2$ by a bump function to extend it to $M$ then 0 will not be a regular value (since the function will be identically zero off of $N$).
Apr
21
answered What is the second stiefel whitney class of SO(n)?
Apr
21
asked Showing a hypersurface is contained in a level set of a regular value