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Jonathan Beardsley's user avatar
Jonathan Beardsley's user avatar
Jonathan Beardsley's user avatar
Jonathan Beardsley
  • Member for 14 years
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Lazard's $\Gamma_n(f)$ as cocycle
@user36938 Hm okay, yeah, no I agree, I have some sort of strange terminology there.
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Lazard's $\Gamma_n(f)$ as cocycle
@user36938 I probably shouldn't say polynomial 3-cochain, I just meant that it's not yet clear that it's a cocycle, so it's a cochain.
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Lazard's $\Gamma_n(f)$ as cocycle
Sorry, yes, I forgot to mention that as part of the hypothesis. I certainly have been using that.
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How does the work of a pure mathematician impact society?
Are you familiar with Gunnar Carllson's company Ayasdi, which is using algebraic topology to solve real world problems successfuly?
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"Symmetric" Polynomial 4-cocycles
Thanks @Dietrich, so you're not aware of any other results regarding polynomials which are "killed" by certain permutations? I sort of wonder if this is connected to the Hodge decomposition and filtration that Loday gives for Hochschild (co)homology.
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"Symmetric" Polynomial 4-cocycles
@YemonChoi So, it's living in something like the cobar construction on $R[x]$, or you can think of it as being in $H^*(\mathbb{G}_a,\mathbb{G}_a)$ where the first is a monoid acting trivially on the module on the right, as described by Demazure and Gabriel. I don't really know of another way to place polynomial cocycles inside of some Hochschild cohomology.
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Are overlaps among {algebraic geometry, arithmetic geometry, algebraic number theory} growing?
Don't forget homotopy theorists. We frequently make excursions into all of those fields and steal things. I don't know what that means though.
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Explicit formula for associator of commutative power series
Wow @Lubin I'd love to talk to you more about this if you'd be willing. It specifically concerns the cohomology theory you and John Tate describe the first two degrees of in your 1966 paper, specifically, the third degree of that cohomology theory. I am essentially trying to reprove a theorem of Lazard's from a purely homological standpoint.
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Explicit formula for associator of commutative power series
Ping me in the homotopy-theory chat if you want the mathematica notebook I wrote to compute these things for finite degrees. Or if you just want to see the polynomials.
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Explicit formula for associator of commutative power series
FWIW I have completely determined this power series up to degree 5, and there is definitely a pattern (although the first 3 degrees are 0 if $f$ is commutative).
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34 35
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