Talk:Supermanifold

different definitions[edit]

There seem to be numerous different definitions of supermanifolds in the literature. It would be useful if this article could give an overview of all the different definitions (with references) and reasons why some may be preferred over others. The field seems young enough that perhaps Wikipedia shouldn't pick out one definition as the correct one. -- Fropuff 00:24, 2 December 2005 (UTC)[reply]

The definition in terms of ringed spaces is very much canonical --Tiphareth

Perhaps, but it would be nice to have more discussion of the less sheaf-theoretic view of supermanifolds. For example, the work of Alice Rogers or B. or C. DeWitt. Mryacht 15:22, 4 November 2006 (UTC)[reply]

well I don't mind the sheafs, they're a great way of thinking, but I am still a bit at loss about this definition. Does anybody have a source? I am looking for a math book on this topic for quite some time (and I consider DeWitts book as a physics book, he doesn't seem to prove existence of Grassmann numbers). What is quite unclear to me in this definition is, what is Lambda^dot(., ..,)? Lambda (in my world) would be the exterior algebra maybe on a vectorspace fibre bundle. But what is ^dot? The space of all morphisms? Until this is resolved, I think it is quite bold to speak of having a 'definition'. Anybody can help? Andreask 09:45, 14 June 2007 (UTC) Supersymmetry for Mathematicians: An Introduction,V. S. Varadarajan,http://www.amazon.com/Supersymmetry-Mathematicians-Introduction-Courant-Lecture/dp/0821835742/ref=sr_1_1?ie=UTF8&s=books&qid=1288555817&sr=8-1 dedwards@math.uga.edu. —Preceding unsigned comment added by Davidaedwards (talk • contribs) 20:12, 31 October 2010 (UTC)[reply]

what about the morphisms?[edit]

supermanifolds together with their maps form a category. Hence the morphisms between them really matters and should be stated in the article as well... — Preceding unsigned comment added by Mircomaster (talk • contribs) 12:05, 17 October 2011 (UTC)[reply]

Remove oddball comment[edit]

I am removing this comment, which has been in the article since it's very creation:

Side comment

This is different from the alternative definition where, using a fixed Grassmann algebra Λ generated by a countable number of generators, one defines a supermanifold as a point set space using charts with the "even coordinates" taking values in the linear combination of elements of Λ with even grading and the "odd coordinates" taking values which are linear combinations of elements of Λ with odd grading. This raises the question of the physical meaning of all these Grassmann-valued variables. Many physicists claim that they have none and that they are purely formal; if this is the case, this may make the definition in the main part of the article preferable.

I'm removing it because it doesn't make sense. The only definition I know of that makes sense is that in Bryce DeWitts book "Supermanifolds", and, from what I can tell, the above paragraph seems to be describing a one-dimensional superspace. To the best of my knowledge, this si not used anywhere in any textbook I know of. So I'm just removing it as some kind of old cruft that doesn't quite really make sense. 67.198.37.16 (talk) 03:09, 2 October 2016 (UTC)[reply]

Oh. I think I just now understood what that was trying to say. I wrote a section that now says that, but in a more concrete and direct way. 67.198.37.16 (talk) 04:20, 2 October 2016 (UTC)[reply]