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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• Added pointers concerning the suggestion that the observed Higgs mass is related to asymptotic safety.

• tried to polish a little and slightly expand model category, starting with the Definition-section and ending with the (new and tiny) Properties section. Added some more subsections and so on.

• Added redirects and a description of other contributions.

• books

• Removed an incorrect historical claim (Dwyer and Kan did throughly investigate relative categories already in 1980s, way before 2000s).

• Page created, but author did not leave any comments.

• Geometry Gems is no longer available

HieronymousCoward

• Hello, I added some words about an ambiguity I found in the literature about the name “dilatino”. If I am wrong, I’d be thankful to the one who makes me notice the mistake!

• need the link, but nothing here yet

• Previous edit is mine.

• stated the definition $\Delta f = \star d \star d f$ and spelled out how this gives the usual component formula:

\begin{aligned} \star d \star d f & = \star d \star (\partial_j f) d x^j \\ & = \star d \left( \tfrac{1}{ \color{green} (D-1)! } \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } \, g^{ i j} (\partial_j f) \, \epsilon_{ i {\color{green} k_2 \cdots k_{D} } } d x^{ \color{green} k_2 } \wedge \cdots \wedge d x^{ \color{green} k_{D} } \right) \\ & = \star \partial_{ \color{magenta} k_1} \left( \tfrac{1}{ \color{green} (D-1)! } \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } \, g^{i j} (\partial_j f) \, \epsilon_{ i {\color{green} k_2 \cdots k_{D} } } d x^{ \color{magenta} k_1 } \wedge d x^{ \color{green} k_2 } \wedge \cdots \wedge d x^{ \color{green} k_{D} } \right) \\ & = \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } \underset{ = \det\big( (g_{i j})^{-1} \big) \delta^{ \color{magenta} k_1 }_i }{ \underbrace{ \tfrac{1}{ { \color{orange} D! } { \color{green} (D-1)! } } \epsilon_{ \color{orange} l_1 l_2 \cdots l_D } g^{ { \color{orange} l_1 } { \color{magenta} k_1 } } g^{ { \color{orange} l_2 } { \color{green} k_2 } } \cdots g^{ { \color{orange} l_D} { \color{green} k_D } } \epsilon_{ i {\color{green} k_2 \cdots k_{D} } } } } \, \partial_{ \color{magenta} k_1 } \left( \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } g^{i j} (\partial_j f) \right) \\ & = \frac{1}{ \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } } \delta^{ \color{magenta} k_1 }_i \partial_{ \color{magenta} k_1 } \left( \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } g^{i j} (\partial_j f) \right) \\ & = \frac{1}{ \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } } \partial_{i} \left( \sqrt{ \left\vert det\big( (g_{i j}) \big) \right\vert } g^{i j} (\partial_j f) \right) \end{aligned}
• expanded brane

first a little remark on what D-branes are abstractly, in reply to an MO-question, then something on fundamental branes, going along with the discussion on the Café

• brief category:people entry in order to make hyperlinks work

• Hello,

I noticed DFT page has not been updated in a while and I added a couple of sections: some sketchy introductory material (analogy between Kaluza-Klein and DFT) and a little insight about a more rigorous geometrical formulation of DFT.

It is still quite sketchy but I would be happy to refine it.

PS: this is my first edit, I hope I played by the rules. And thank you all for this wiki

Luigi

• starting something

I interlinked that with the entry Kan fibrant replacement, where the subdivision $nerve \circ Face$ appears.

• The entry Clifford algebra used to state the classification and Bott periodicty over the complex numbers, but not over the real numbers. I have added in now the relevant statements, straight from Lawson-Michelson:

Just the bare statements so far.

• added some very basic facts on $SU(2)$ here to special unitary group. Just so as to be able to link to them.

• I added some discussion to Hausdorff space of how the localic and spatial versions compare in classical and constructive mathematics, including in particular the fact that I just learned (in discussion with Martin Escardo and Andrej Bauer) that a discrete locale is Hausdorff iff it has decidable equality.

• added a table (here) showing the first-generation mesons as irreps of the spacetime $\times$ isospin symmetry group

• Add a note about “Daniel’s answer” to the semantics-structure question. The discussion on this page should really be merged into the main text and archived at the forum.

• a stub, for completeness