Increasing trees and Kontsevich cycles. (English) Zbl 1069.57008

Following on from the first author’s paper [Topology 43, 1469–1510 (2004; Zbl 1069.57007)], the authors give a recursive formula for all the coefficients in the polynomial expressing the Kontsevich cycles in graph cohomology in terms of the Miller-Morita-Mumford classes in the cohomology of mapping class groups.


57M99 General low-dimensional topology
55R40 Homology of classifying spaces and characteristic classes in algebraic topology
05C05 Trees
57N05 Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010)


Zbl 1069.57007
Full Text: DOI arXiv EuDML EMIS


[1] E Arbarello, M Cornalba, Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves, J. Algebraic Geom. 5 (1996) 705 · Zbl 0886.14007
[2] M Culler, K Vogtmann, Moduli of graphs and automorphisms of free groups, Invent. Math. 84 (1986) 91 · Zbl 0589.20022
[3] J Conant, K Vogtmann, On a theorem of Kontsevich, Algebr. Geom. Topol. 3 (2003) 1167 · Zbl 1063.18007
[4] K Igusa, Combinatorial Miller-Morita-Mumford classes and Witten cycles, Algebr. Geom. Topol. 4 (2004) 473 · Zbl 1072.57013
[5] K Igusa, Higher Franz-Reidemeister torsion, AMS/IP Studies in Advanced Mathematics 31, American Mathematical Society (2002) · Zbl 1016.19001
[6] K Igusa, Graph cohomology and Kontsevich cycles, Topology 43 (2004) 1469 · Zbl 1069.57007
[7] K Igusa, Higher complex torsion and the framing principle, Mem. Amer. Math. Soc. 177 (2005) · Zbl 1083.57030
[8] M Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992) 1 · Zbl 0756.35081
[9] E Y Miller, The homology of the mapping class group, J. Differential Geom. 24 (1986) 1 · Zbl 0618.57005
[10] G Mondello, Combinatorial classes on \(\mathcalM_{g,n}\) are tautological, Int. Math. Res. Not. (2004) 2329 · Zbl 1069.14026
[11] S Morita, Characteristic classes of surface bundles, Bull. Amer. Math. Soc. \((\)N.S.\()\) 11 (1984) 386 · Zbl 0579.55006
[12] M Petkov\vsek, H S Wilf, D Zeilberger, \(A=B\), A K Peters Ltd. (1996)
[13] R Stenli, Perechislitelnaya kombinatorika, “Mir” (1990) 440
[14] K Strebel, Quadratic differentials, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], Springer (1984) · Zbl 0547.30001
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