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bio website math.berkeley.edu/~cgerig
location UC Berkeley
age 25
visits member for 3 years, 11 months
seen 13 mins 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 student of Michael Hutchings!


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revised Companion to theoretical physics for working mathematicians
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revised Companion to theoretical physics for working mathematicians
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revised Companion to theoretical physics for working mathematicians
added 724 characters in body
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revised Companion to theoretical physics for working mathematicians
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answered Companion to theoretical physics for working mathematicians
Dec
11
comment Symplectic Submanifolds of Contact Manifolds and Contact Submanifolds of Symplectic Manifolds
You can hope for a hypersurface and a chosen primitive for $\omega$ in a neighborhood of it. This is in the spirit of the "canonical" example $(M,\lambda)\subset (\mathbb{R}\times M,d(e^s\lambda))$.
Nov
24
comment Inverted pair of complex analytic families
I don't quite understand the dictionary between the referenced paper and the problem here, can you explain further?
Nov
23
revised Inverted pair of complex analytic families
added 416 characters in body
Nov
22
reviewed Approve combinatorial-game-theory tag wiki
Nov
19
revised Inverted pair of complex analytic families
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Nov
19
revised Embedded Contact Homology and Manifold Decompositions
added 257 characters in body
Nov
19
answered Embedded Contact Homology and Manifold Decompositions
Nov
17
asked Inverted pair of complex analytic families
Nov
2
awarded  Popular Question
Oct
23
comment Why the Dold-Thom theorem?
I don't, but I also tend not to gain intuition by making things more abstract (that's a statement about me). Jesse's answer, along with the comments under the question, does seem to provide an intuition about the two things directly; although I will admit that I prefer something similar in spirit to Ryan's suggestion.
Oct
23
accepted Why the Dold-Thom theorem?
Oct
23
comment Why the Dold-Thom theorem?
OK, if I buy this and $S_f$'s existence, then to get an element of $X$'s homology, I take the composition $S_f\hookrightarrow S^i\times X\twoheadrightarrow X$ and push-forward the image of the fundamental class $[S_f]$? Why would this be the "correct" element?
Oct
23
revised Why the Dold-Thom theorem?
Consolidating the important comments
Oct
23
comment Why the Dold-Thom theorem?
So I think this response shifts my question onto another isomorphism, and my question is then: "Why is $\pi_*(F(X))\cong \widetilde{kO}_*(X)$ true, intuitively?" I see a proof of the isomorphism, but I think it skirts my question.
Oct
22
comment Why the Dold-Thom theorem?
I'm sorry I cant' wrap my head around this yet, even for $i=1$. In the first paragraph, $k$ can't vary across the cells of $S^i$, right? And I don't see how the "subspace" of $S^i\times X$ come together to form a CW-complex. I also didn't understand the last sentence; how does the map $S_f\to S^i$ relate to "lifted maps to $X^k$"? And how do I ultimately get an element of homology of $X$?