Abstract
A proof of the Hanna Neumann conjecture (HN-conjecture) based on the ideas of Mineyev andDicks is presented. The new ingredients are theQuillen formula for the Euler–Poincaré characteristic and the “abstract HN-conjecture.”
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References
H. Neumann, “On the intersection of finitely generated free groups,” Publ. Math. Debrecen 4, 186–189 (1956).
I. Mineyev, “Submultiplicativity and the Hanna Neumann conjecture,” Ann. of Math. (2) 175 1, 393–414 (2012).
J. Friedman, Sheaves on Graphs and a Proof of the Hanna Neumann Conjecture (2011), http://wwwmathubcca/~jf/pubs/web_stuff/mehannahtml.
Y. A. Pichel, Dicks’ Simplification of Mineyev’s Proof of the SHNC, http://wwwpersonalsotonacuk/am1t07/ggt/Antolin-talk. pdf.
M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of the Theory of Groups, 4th ed. (Nauka, Moscow, 1996; English transl. of the 2nd ed. Springer-Verlag, New York–Berlin, 1979).
J.-P. Serre, Trees (Springer-Verlag, Berlin, 1980).
M. Culler and J. W. Morgan, “Group actions on R-trees,” Proc. London Math. Soc. 55 3, 571–604 (1987).
J.-P. Serre, “Cohomologie des groupes discrets,” in Prospects in Mathematics, Ann. of Math. Studies (Princeton Univ. Press, Princeton, NJ, 1971), Vol. 70, pp. 77–169.
Yu. I. Manin, “Good proofs are proofs that make us wiser,” Mitteilungen der DMV 2, 40–44 (1998).
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Original Russian Text © G. A. Noskov, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 3, pp. 376–383.
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Noskov, G.A. Mineyev–Dicks proof of the HN-conjecture and the Euler–Poincaré characteristic. Math Notes 99, 390–396 (2016). https://doi.org/10.1134/S000143461603007X
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DOI: https://doi.org/10.1134/S000143461603007X