Gelfand, I. M.; MacPherson, Robert D. Geometry in Grassmannians and a generalization of the dilogarithm. (English) Zbl 0504.57021 Adv. Math. 44, 279-312 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 60 Documents MSC: 57T15 Homology and cohomology of homogeneous spaces of Lie groups 57R20 Characteristic classes and numbers in differential topology 58A10 Differential forms in global analysis 32M10 Homogeneous complex manifolds 32L20 Vanishing theorems 57S25 Groups acting on specific manifolds Keywords:analytic and geometric properties of Grassmann simplices; polyhedra in the Grassmann manifolds; differential forms which generalize the classic dilogarithm; stable characteristic class for real vector bundles; Pontrjagin character forms; functional equation for the dilogarithm; tetrahedral complex Citations:Zbl 0312.57015; Zbl 0312.57016; Zbl 0341.57017 PDFBibTeX XMLCite \textit{I. M. Gelfand} and \textit{R. D. MacPherson}, Adv. Math. 44, 279--312 (1982; Zbl 0504.57021) Full Text: DOI References: [1] K. Aomoto; K. Aomoto · Zbl 0545.33014 [2] Aomoto, K., A generalization of Poincaré normal function on a polarized manifold, Proc. Japan Acad. Ser. A, Math. Sci., 55, No. 9, 353-358 (1975) · Zbl 0453.14011 [3] Atiyah, M. F., Convexity and commuting Hamiltonians (1981), Oxford University, preprint · Zbl 0482.58013 [4] Beilinson, A., Algebraic \(k\)-theory and values of \(L\) functions (1980), preprint, Moscow [5] Binet, J., Mémoire sur la théorie des axes conjugués et des moments d’inertie des corps, J. École Polytechn., 9, No. 16, 41-67 (1811) [6] Bloch, S., Applications of the dilogarithm function in algebraic \(k\)-theory and algebraic geometry, (Proceedings, Int. Symp. on Algebraic Geometry. Proceedings, Int. Symp. on Algebraic Geometry, Kyoto (1977)), 103-114 [7] Bol, G., Über ein bemerkensvertes Funfgewebe in der Ebene, Abh. Math. Sem. Univ. Hamburg., 11, 393 (1935) · JFM 62.0830.01 [8] Damiano, D. B., Webs, Abelian equations, and characteristic classes, (Thesis (May 1980), Brown University) [9] Damiano, D. B., Webs and characteristic forms of Grassmann manifolds (1981), Princeton University, preprint [10] Russian Math. Surveys, 33, No. 2, 97-154 (1978), Trans. · Zbl 0425.14013 [11] Euler, L., De summatione serierum in hac formo contenlarum \(a1 + a^24 + a^39 + a^416\) + …\), Mém. Acad. St. Petersberg Bd., 3, 26-42 (1779) [12] Goodwillie, T., Volume and dilogarithm (1979), notes [13] B. Gross; B. Gross [14] Gabrielov, A. M.; Gelfand, I. M.; Losik, M. V., Combinatorial Calculation of Characteristic Classes, Functional Analysis and Its Applications, No. 3, 5-26 (1975), [In Russian] · Zbl 0312.57015 [15] Heckman, G. J., Projections of orbits and asymptotic behaviour of multiplicities for compact Lie groups, (thesis (1980)), Leiden · Zbl 0497.22006 [16] Hirzebruch, F., Neue Topologischen Methoden in der Algebraischen Geometrie (1962), Springer-Verlag: Springer-Verlag Berlin [17] Klein, F.; Lie, S., Sur une certaine famille de courbes et de surfaces, C. R. Acad. Sci. Paris, 1275-1279 (1870) · JFM 02.0632.01 [18] Lewin, L., Dilogarithms and Associated Functions (1958), MacDonald: MacDonald London · Zbl 0083.35904 [19] MacPherson, R. D., The Combinatorial Formula of Gabrielov, Gelfand, and Losik for the First Pontrjagin Class, Sem. Bourbaki, No. 497 (1976/1977) [20] Milnor, J., Computation of volume, (Thurston, W. P., The Geometry and Topology of Three-Manifolds (1980), Princeton Mathematics Department), Chap. 7 [21] Milnor, J.; Stasheff, J., Characteristic Classes, Annals of Mathematics Studies No. 76 (1974), Princeton N.J. · Zbl 0298.57008 [22] Rogers, L. J., On function sum theorems connected with the series \(∑^∞n = 1x^n n^2\), (Proc. London Math. Soc., 4 (1907)), 169-189 · JFM 37.0428.03 [23] Spence, W., An essay on logarithmic transcendents (1809), London and Edinburgh [24] D. Wigner; D. Wigner [25] Yusin, B. V., Sur les formes \(S^{p,q}\) apparaissant dans le calcul combinatoire de la \(2^e\) classe de Pontrjagin par la méthode de Gabrielov, Gelfand et Losik, C. R. Acad. Sci. Paris (1981), Ser. A · Zbl 0469.57018 [26] Zindler, K., Die Tetraedralen und die anderen Kollineationskomplexe, Encyklopädie der Mathematischen Wissenschaften, Band 3, 1150-1161 (1928), Teil 2 [27] Berezin, F. A.; Gelfand, I. M., Some remarks on the theory of spherical functions on symmetric Riemannian manifolds, Trudy Moskov. Mat. Obšč., 5, 311-351 (1956) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.