共查询到20条相似文献,搜索用时 15 毫秒
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Let P→B be a principal G-bundle. For any connection θ on P, the Chern-Weil construction of characteristic classes defines an algebra homomorphism from the Weil algebra Wg=Sg∗⊗∧g∗ into the algebra of differential forms A=Ω(P). Invariant polynomials inv(Sg∗)⊂Wg map to cocycles, and the induced map in cohomology inv(Sg∗)→H(Abasic) is independent of the choice of θ. The algebra Ω(P) is an example of a commutativeg-differential algebra with connection, as introduced by H. Cartan in 1950. As observed by Cartan, the Chern-Weil construction generalizes to all such algebras.In this paper, we introduce a canonical Chern-Weil map Wg→A for possibly non-commutativeg-differential algebras with connection. Our main observation is that the generalized Chern-Weil map is an algebra homomorphism “up to g-homotopy”. Hence, the induced map inv(Sg∗)→Hbasic(A) is an algebra homomorphism. As in the standard Chern-Weil theory, this map is independent of the choice of connection.Applications of our results include: a conceptually easy proof of the Duflo theorem for quadratic Lie algebras, a short proof of a conjecture of Vogan on Dirac cohomology, generalized Harish-Chandra projections for quadratic Lie algebras, an extension of Rouvière's theorem for symmetric pairs, and a new construction of universal characteristic forms in the Bott-Shulman complex. 相似文献
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R. D. Katamadze 《Journal of Mathematical Sciences》2008,152(3):323-329
As is known, the homology and cohomology Massa-Takasu groups for pairs of groups (G, H) are defined by the embedding f: H → G, H < G [2].
In our case, these definitions are extended to an arbitrary group homomorphism φ: Π → G. In particular, we define homology and cohomology groups of the nth order for the homomorphism φ, and if Π = H, we obtain the known theory [2].
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 43, Topology
and Its Applications, 2006. 相似文献
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The restricted homomorphism problem asks: given an input digraph G and a homomorphism g:G→Y, does there exist a homomorphism f:G→H? We prove that if H is hereditarily hard and YH, then is NP-complete. Since non-bipartite graphs are hereditarily hard, this settles in the affirmative a conjecture of Hell and Nešetřil. 相似文献
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José Carlos de Souza Kiihl 《Rendiconti del Circolo Matematico di Palermo》1980,29(3):411-419
In this paper we develop a technique to study the homomorphisma: MU * (B U1)→M U*?2 (B U1) defined by assigning to the class off: M→B U 1 the class off oi: N→B U1, wherei: N→M is the submanifold dual tof*(γ1)?f*(γ1), and γ1→B U is the 3 universal line boundle. So that we can present a (σn), where σnis the class of the classifying map of the canonical line boundle overC P n, in terms of the σi’s and chosen generators of Π★(M U). 相似文献
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We prove that the lower bounds for Betti numbers of the rack, quandle and degeneracy cohomology given in Carter et al. (J. Pure Appl. Algebra, 157 (2001) 135) are in fact equalities. We compute as well the Betti numbers of the twisted cohomology introduced in Carter et al. (Twisted quandle cohomology theory and cocycle knot invariants, math. GT/0108051). We also give a group-theoretical interpretation of the second cohomology group for racks. 相似文献
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Ivan Kolá 《Annals of Global Analysis and Geometry》1993,11(1):41-47
We determine all gauge-natural forms on a principal fiber bundle with values in an arbitrary associated vector bundle, which generalize the classical Chern-Weil forms. 相似文献
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Let $\mathfrak{F}_{\lambda}^{n}$ be the $\mathop {\mathfrak {osp}}\nolimits \,(n|2)$ -module of weighted densities on ?1|n of weight ??. We compute the cohomology spaces $\mathrm{H}^{k}_{\mathrm{diff}}\left(\mathop {\mathfrak {osp}}\nolimits \,(n|2),\mathfrak{F}_{\lambda}^{n}\right)$ , where k=1 and n=0,1,2 or k=2 and n=0,1. We explicitly give cocycles spanning these cohomology spaces. 相似文献
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