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

• renamed from “geometric fixed points” to “geometric fixed point spectrum”, which is clearly the better/right entry title

• Updating reference to cubical type theory. This page need more work.

• Provided a bare minimum so as to ungrey the link. Feel free to expand/correct.

• Order-theoretic version

• made explicit that for a normal subgroup $N \subset G$ its “Weyl group” in the sense of $W_H G \coloneqq (N_G H)/H$ coincides with the plain quotient group $G/N$.

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

Anonymous

• I am trying to imrpove the complex of entries revolving around the Hurwitz theorem. I am not done yet at all, but since in the process I am touching a lot of entries, I thought I’d drop a note now for those anxiously following the RecentlyRevised notifications.

So I gave Hurwitz theorem its own entry, first of all, cross linking to the details (a proof,in fact), that may be found at composition algebra, but which previously could not be found from normed division alegbra. Now there are cross-links.

I also tried to add more references, but this needs work. It seems that Wikipedia says both that the source is

• Adolf Hurwitz, Über die Composition der quadratischen Formen von beliebig vielen Variabeln, Nachr. Ges. Wiss. Göttingen (1898) 309–316

as well as that “was published posthumously in 1923”.

But I haven’t really spent much effort yet to check.

I also added cross-links with Hopf invariant one, but this is plain stubby for the moment.

• Missing page, just a definition

• Stub, hope to write more soon.

• I have added in references to Whitehead’s address ’delivered before the Princeton Meeting of the AM Society on November 2, 1946’ that is ‘combinatorial homotopy 1’.

• rewrote the Idea-section from scratch

• Fix $k = 0$ case of vector-valued cross products (one for each unit vector).

• After typing [[fixed point]]-spaces in various entries, I finally decided that “fixed point space” should have an entry of its own, with some comments and further pointers, if only for ease of hyperlinking.

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

• Other terminology

• Added a definition, generalization to (hyper)surfaces

• made sub-sections for the different definitions; slightly expanded the definition in terms of differential forms (here)

• Corrected an arithmetic error in the last section.

• have re-touched the formatting of this ancient entry from the early days of the $n$Lab, and added hyperlinks and cross-links

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

• minimum on the multicategory of permutative categories, for the moment just as to record references and make hyperlinks work

• Included some links to his theses and a start on his papers.

• Unfortunately, I need to discuss with you another terminological problem. I am lightly doing a circle of entries related to combinatorial aspects of representation theory. I stumbled accross permutation representation entry. It says that the permutation representation is the representation in category $Set$. Well, nice but not that standard among representation theorists themselves. Over there one takes such a thing – representation by permutations of a finite group $G$ on a set $X$, and looks what happens in the vector space of functions into a field $K$. As we know, for a group element $g$ the definition is, $(g f)(x) = f(g^{-1} x)$, for $f: X\to K$ is the way to induce a representation on the function space $K^X$. The latter representation is called the permutation representation in the standard representation theory books like in

• Claudio Procesi, Lie groups, an approach through invariants and representations, Universitext, Springer 2006, gBooks

I know what to do approximately, we should probably keep both notions in the entry (and be careful when refering to this page – do we mean representation by permutations, what is current content or permutation representation in the rep. theory on vector spaces sense). But maybe people (Todd?) have some experience with this terminology.

Edit: new (related) entries for Claudio Procesi and Arun Ram.