5,490 reputation
22163
bio website math.berkeley.edu/~cgerig
location UC Berkeley
age 26
visits member for 4 years, 2 months
seen 6 hours ago

After doing my BS in engineering physics, I started my PhD in experimental atomic physics. But I quit to do math, and am now a 3rd year student of Michael Hutchings.

I greatly thank Allen Hatcher for his recommendation letter which pulled me into college, after learning algebraic topology through his book in high school.


2d
answered Why not develop a Hamiltonian-based Morse theory?
Mar
27
comment Mathematical statistical qm book-recommendation
Quantum Physics: A Functional Integral Point of View by Glimm and Jaffe (they're theoretical physicists). That's the closest I can think of, which should suffice since it is rigorous, but I find it hard to follow (they leave a lot up to the reader).
Mar
20
comment Pseudomanifolds and Poincaré duality
Oh I thought "Poincare duality space" just meant $H^k\approx H_{n-k}$ and not necessarily induced by maps, sorry.
Mar
20
comment Pseudomanifolds and Poincaré duality
Ah, the "kissing banana" is not a pseudomanifold (doesn't satisfy second bullet point), nevermind!
Mar
19
revised $\pi_0${plane fields}$\to\mathbb{Z}_2$
added 76 characters in body
Mar
18
reviewed Reject A metric for Grassmannians
Mar
16
answered What if the low-degree cohomology of a $G$-module and all its restrictions vanish?
Mar
4
comment Elliptic operators corresponds to non vanishing vector fields
Yes; I think the spherical harmonics won't be in the image, because they can't be integrated (when solving for the corresponding function in the domain). For example, in order for $D_X(f)=\cos\phi$ you need $f=\sin^2\theta\ln|\sin\phi|$ which blows up at $\phi=0,\pi$.
Feb
24
comment Elliptic operators corresponds to non vanishing vector fields
@AliTaghavi, I think the cokernel is infinite-dimensional.
Feb
24
comment liftings of principal bundles
OK, what then makes the coefficient system constant when $K$ is central? Some sort of reduction map must be arising somewhere?
Feb
23
comment liftings of principal bundles
Can you explain why local coefficients are required when $K$ is abelian but not central?
Feb
23
revised Coboundary of a cup-product
rolled back to a previous revision
Feb
23
revised Coboundary of a cup-product
added 232 characters in body
Feb
23
revised Coboundary of a cup-product
added 232 characters in body
Feb
23
comment Coboundary of a cup-product
True, but an exercise in that book gives this as a special case to a more general "stability" result, which I was hopeful would be of use here. And I now agree with Neil's comment. I was originally equating $H^\ast(X\times A,A\times A)$ with $H^\ast(X,A)$ and I no longer hold that in my mind.
Feb
23
revised Coboundary of a cup-product
added 555 characters in body
Feb
23
revised Coboundary of a cup-product
deleted 360 characters in body
Feb
23
revised Coboundary of a cup-product
added 360 characters in body
Feb
23
comment Coboundary of a cup-product
Sure there is, see chapter VII section 8 of Dold's Lectures on Algebraic Topology, where $(X,A,\varnothing)$ is an excisive triad. The "stability" property 8.10 seems highly relevant.
Feb
23
revised Coboundary of a cup-product
mainly removed a redundant sentence