A classifying space for commutativity in Lie groups
نویسندگان
چکیده
منابع مشابه
Vector Bundles over Classifying Spaces of Compact Lie Groups
The completion theorem of Atiyah and Segal [AS] says that the complex K-theory group K(BG) of the classifying space of any compact Lie group G is isomorphic to R(G)̂ : the representation ring completed with respect to its augmentation ideal. However, the group K(BG) = [BG,Z × BU ] does not directly contain information about vector bundles over the infinite dimensional complex BG itself. The purp...
متن کاملHomotopy Theory of Lie groups and their Classifying Spaces
1. Lie groups, homomorphisms and linear representations. Irreducible representations. 2. Maximal tori in compact Lie groups. 3. Characters of representations. Ring of virtual characters. The Weyl theorem. 4. Actions of Lie groups. Homogeneous spaces (orbits) and equivariant maps. 5. Classifying spaces of topological groups and maps induced by homomorphisms. 6. Homotopy classification of maps be...
متن کاملSelf-maps of Classifying Spaces of Compact Simple Lie Groups
We describe here the set [BG, BG] of homotopy classes of self-maps of the classifying space BG , for any compact connected simple Lie group G. In particular, we show that two maps ƒ , f : BG —• BG are homotopic if and only if they are homotopic after restricting to the maximal torus of G ; or equivalently if and only if they induce the same homomorphism in rational cohomology. In addition, we i...
متن کاملHomotopy Theory of Classifying Spaces of Compact Lie Groups
The basic problem of homotopy theory is to classify spaces and maps between spaces, up to homotopy, by means of invariants like cohomology. In the last decade some striking progress has been made with this problem when the spaces involved are classifying spaces of compact Lie groups. For example, it has been shown, for G connected and simple, that if two self maps of BG agree in rational cohomo...
متن کاملCommutativity in non-Abelian Groups
Let P2(G) be defined as the probability that any two elements selected at random from the group G, commute with one another. If G is an Abelian group, P2(G) = 1, so our interest lies in the properties of the commutativity of nonAbelian groups. Particular results include that the maximum commutativity of a non-Abelian group is 5/8, and this degree of commutativity only occurs when the order of t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2015
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2015.15.493