Chris Gerig
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Registered User
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Engineering Physics major from Cornell, and studied gravity (at small distances) as a low-temperature experimental physics researcher...... now I'm just behind in math.
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4h |
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About the curvature of a connection? Future reference: this is not appropriate for MO, and should be asked on Math StackExchange. |
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May 5 |
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Does a connected manifold with vanishing Euler characteristic admit a nowhere-vanishing vector field? (It's due to Poincare and Hopf and called their index theorem.) |
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May 3 |
awarded | ● Popular Question |
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May 1 |
answered | Vector fields on $(4n+1)$-spheres |
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Apr 30 |
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Vector fields on $(4n+1)$-spheres Correct, but this is what sparked my questions. |
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Apr 30 |
awarded | ● Nice Question |
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Apr 30 |
revised |
Vector fields on $(4n+1)$-spheres added 688 characters in body; deleted 1 characters in body |
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Apr 30 |
revised |
symbol map in algebraic K theory edited tags |
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Apr 30 |
asked | Vector fields on $(4n+1)$-spheres |
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Apr 20 |
answered | A basic question related to Hamiltonian isotopy in symplectic geometry |
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Apr 19 |
answered | Finite dimensional “Mountain Pass Lemma” |
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Apr 18 |
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Generalized geometry and spin structures @Pedro: Yes I agree (the 'doubling' disappearing over the 1-skeleton for the spin structures); this is the way to get around the noncanonical-ness of using $TM$ instead of $T^*M$. I hope this was of help! |
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Apr 15 |
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What is “Data” involved in a mathematical construction? It means what Webster's dictionary says it means. |
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Apr 5 |
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The second homology of a group G and presentation complex of G Group-cohomology encompasses group homology; the previous tag is more abundant. |
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Apr 4 |
awarded | ● Popular Question |
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Apr 4 |
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geometric meaning of Ricci-flatness math.stackexchange.com/questions/339057/… ... I suggest making an edit to your post on the other site, so that you can receive better help. |
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Apr 4 |
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Two ways of getting a cohomology class from an extension of a discrete group by $\mathbb C^*$ Addendum: This fibration I think is a principal bundle, and so existence of a section would mean the bundle is trivial, which should mean that the cohomology class in $H^2$ is zero, so that its image in $H^3$ is also zero, giving agreement here. |
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Apr 4 |
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Two ways of getting a cohomology class from an extension of a discrete group by $\mathbb C^*$ Also, your extension $\alpha$ corresponds to the $B\mathbb{C}^*$-fibration that you write, and so we want an explicit description, in terms of the underlying groups, of the failure of a set-theoretic section to be the desired map. Ideally this will have either a cocyle-description (and then check it with $\delta\alpha$) or a crossed module extension description (and then compare extensions). On afterthought, these comments are probably recasting your question into a harder one. |
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Apr 4 |
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Two ways of getting a cohomology class from an extension of a discrete group by $\mathbb C^*$ Just in case you haven't already looked in this direction (I got stuck): $H^3(A,B)$ corresponds to crossed module extensions. So your extension $\alpha\in H^2(G,\mathbb{C}^*)$ maps under the connecting homomorphism to a particular $\mathbb{Z}\to N\to E\to G$, which ideally you can read off from the definitions (with the help of MacLane's paper on this notion). |
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Apr 3 |
accepted | Automorphisms of non-abelian groups of order p^3 |
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Mar 26 |
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Sum of two tangent bundles of $S^{2n}$ added 139 characters in body |
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Mar 26 |
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Sum of two tangent bundles of $S^{2n}$ Ah I took "sum" as direct product, although $\oplus$ is standard notation for Whitney sum. |
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Mar 26 |
answered | Sum of two tangent bundles of $S^{2n}$ |
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Mar 21 |
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Coboundaries and Gluing in Cech Cohomology - Intuition? edited tags |
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Mar 15 |
awarded | ● Popular Question |
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Mar 15 |
awarded | ● Nice Question |
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Mar 15 |
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Yang-Mills and Chern-Simons functionals as Morse functions the question originally referred to "other action functionals" but the responses restricted to the two in the title, so perhaps later I will ask about general info on "others"; edited title |
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Mar 15 |
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Fluid mechanics and topology Google search Robert Ghrist and your wishes may come true. |
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Mar 13 |
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Topology, the board game This seems to be less about math and more about creative uses in boardgames, which is why I vote to close. |
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Mar 12 |
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Quotient of trivial bundles Taking that one step further, you can always stabilize by adding trivial summands: $TM\oplus\epsilon^m= \epsilon^N$ and then do your division. |
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Mar 11 |
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What goes wrong for the Sobolev embeddings at $k=n/p$? added 111 characters in body |
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Mar 10 |
awarded | ● Nice Question |
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Mar 9 |
revised |
What goes wrong for the Sobolev embeddings at $k=n/p$? added 314 characters in body; edited title |
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Mar 8 |
asked | What goes wrong for the Sobolev embeddings at $k=n/p$? |
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Mar 8 |
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euler class of the normal bundle and self intersection number This is typically a homework exercise, and I assume $S$ is a surface, where you have a complex line bundle $L\to S$ so that the Euler class is the 1st Chern class which is interpreted as the self-intersection number of the zero-section of $L$. The reason you would consider this splitting of $T_X|_S$ is to achieve the adjunction formula (in dimension 4). |
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Mar 8 |
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Chern numbers via Euler characteristics? edited tags |
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Mar 7 |
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A question on composites of pushforward and pullback Neither $\pi_*$ nor $\pi^*$ is the transfer (which goes in the opposite direction). And you shouldn't accept Russell's answer yet because it isn't correct -- his 1st attempted counter-example with n even doesn't satisfy your hypotheses, and his 2nd counter-example with n odd vacuously satisfies your conclusion (i.e. is not a counter-example). |
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Mar 7 |
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A question on composites of pushforward and pullback @Russell, this still doesn't work because $|\mathbb{Z}_2|$ will kill the 2-torsion, and so the conclusion would be satisfied trivially. |
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Mar 7 |
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A question on composites of pushforward and pullback @Juan that is not enough, because his original example had $S^{2k}$ orientable while $\mathbb{R}P^{2k}$ is nonorientable! You need a condition on the action (luckily for $S^{2k+1}$ the antipodal action has orientable quotient). |
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Mar 7 |
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A question on composites of pushforward and pullback Have you tried just checking definitions at the chain-level?. One thing to quickly note is that we already have transfer maps that satisfy your conclusion. I'm not sure your construction produces the transfer, and so I wouldn't immediately expect your conclusion to hold. (sorry I'm being lazy right now) |
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Mar 7 |
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A question on composites of pushforward and pullback Be careful, we're invoking Poincare-duality and so your spaces have to be orientable. I assume the question wants $X$ oriented and $\pi$ to be orientation-preserving. |
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Mar 7 |
revised |
A question on composites of pushforward and pullback added 126 characters in body; added 7 characters in body |
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Feb 18 |
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what prevents a manifold to be symplectic? For 4-manifolds, to be symplectic you are required to have $1-b^1(X)+b^2_+(X)=\frac{1}{2}(\chi(X)+\sigma(X))\equiv 0$ mod 2. |
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Feb 17 |
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Computing the cardinality of cohomology groups added 13 characters in body |
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Feb 17 |
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Computing the cardinality of cohomology groups Right, forgot to include "there exists $n$" |
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Feb 16 |
revised |
Computing the cardinality of cohomology groups added 450 characters in body; deleted 1 characters in body |
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Feb 16 |
answered | Computing the cardinality of cohomology groups |
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Feb 15 |
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How many proofs that $\pi_n(S^n)=\mathbb{Z}$ are there? added 19 characters in body |
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Feb 14 |
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Transfer map for group homology. edited body |
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Feb 14 |
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Transfer map for group homology. You should check out Ken Brown's textbook Cohomology of Groups, that's the definitive. A nice way to see the transfer is induced from the covering map of classifying spaces. Namely, if $\sigma$ is a cell of $BG$ then $\sum\tilde{\sigma}$ is a cell of $BH$ (i.e. all the lifts of $\sigma$). Then $Tr$ maps cochain $f$ to the cochain $\sigma\mapsto \sum f(\tilde{\sigma})$. |
