String topology of classifying spaces
نویسندگان
چکیده
منابع مشابه
Higher String Topology on General Spaces
In [2], Chas and Sullivan considered the free loop space LM = Maps(S,M) for a smooth orientable compact manifold M . They used geometric methods to show that H∗LM has, among other things, the structure of a Batalin-Vilkovisky algebra. More precisely, C∗LM has an action by the operad of chain complexes C∗D2, where D2 is the framed 2-dimensional little disk operad. Each element of D2(n) is an ord...
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In 1976, Adams & Mahmud 3] published the rst systematic study of the problem of determining the homological properties of maps between classifying spaces of compact connected Lie groups. This was continued in later work by one or both authors: Adams 2] extended some of the results to the case of non-connected Lie groups by using complex K-theory; while Adams & Mahmud 4] identiied further restri...
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If G is a connected compact Lie group, then for almost all prime numbers p the mod p cohomology ring of the classifying space BG is a finitely generated polynomial algebra. In 1961, N. Steenrod [24] asked in general for a determination of all spaces X such that H∗(X,Fp) is a finitely generated polynomial algebra (i.e., such that X has a polynomial cohomology ring); at that time, the only exampl...
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We define algebraic cobordism of classifying spaces, Ω∗(BG) and G-equivariant algebraic cobordism Ω∗G(−) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted F (Ω(−)), which are required for the definition to work. We show that G-equivariant cobordism satisfies the localization exact sequence. We calculate Ω(BG) for algebraic groups...
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We establish the general machinery of string topology for differentiable stacks. This machinery allows us to treat on an equal footing free loops in stacks and hidden loops. In particular, we give a good notion of a free loop stack, and of a mapping stack Map(Y,X), where Y is a compact space and X a topological stack, which is functorial both in X and Y and behaves well enough with respect to p...
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2012
ISSN: 1435-5345,0075-4102
DOI: 10.1515/crelle.2011.140