Abstract
We develop a theory of almost algebraic Poincaré complexes to write an analog of the Hirzebruch formula with nonflat coefficients for combinatorial manifolds.
Similar content being viewed by others
References
Mishchenko, A. S.: Homotopic invariants of non simply connected manifolds. 1. Rational invariants, Izvest. Acad. Sci. USSR Ser. Math. 34(3) (1970), 501-514, in Russian; English translation: Math. USSR Izvest. 4(3) (1970), 506-519.
Mishchenko, A. S. and Solovjov, Ju. P.: Representations of Banach algebras and the Hirzebruch type formulas, Math. Sb. N.S. 111(2) (1980), 209-226, in Russian; English translation: Math. USSR Sb. 39(2) (1981).
Connes, A., Gromov, M. and Moscovoci, H.: Conjecture de Novicov et fibrés presque plats, C. R. Acad. Sci. Paris Sér. I 310 (1990), 273-277.
Hilsum, M. and Skandalis, G.: Invariance par homotopie de la signature a coefficients dans un fibre presque plat, J. Reine Angew. Math. 423 (1992), 72-99.
Roe, J.: Index Theory, Coarse Geometry, and Topology of Manifolds, CBMS, Regional Conf. Ser. in Math. 90, Conf. Board. Math. Sci., Washington, DC, 1996, p. 62.
Ferry, S. C., Ranicki, A. and Rosenberg, J.: A history and survey of the Novikov conjecture, In: Funct. Anal. on the Eve of the 21st Century, Vol. II, Progr. in Math. 132, Birkhauser, Basel; Novikov Conjectures, Index Theorems and Rigidity, Vol. 1 (Oberwolfach, 1993), London Math. Soc. Lecture Notes Ser. 226, Cambridge Univ. Press, 1995, pp. 7-66.
Gromov, M.: Positive curvature, macroscopic dimension, spectral gaps and higher signatures, In: Funct. Anal. on the Eve of the 21st Century, Vol. II, Progr. in Math. 132, Birkhauser, Basel, 1995.
Manuilov, V. M. and Mishchenko, A. S.: Relations between asymptotic and Fredholm representations, Preprint IHES (1997).
Mishchenko, A. S. and Noor, M.: Asymptotic representations of discrete groups, In: Lie Groups and Lie Algebras. Their Representations, Generalizations and Applications, Math. Appl. 433. Kluwer Acad., Dordrecht, 1998, pp. 299-312; Math. Rev.: 1630585.
Manuilov, V. M. and Mishchenko, A. S.: Asymptotic and Fredholm representations of discrete groups, Math. Sb. 189(10) (1998), 53-74, in Russian; English transl. Sb. Math. 189(10) (1998), 1485-1504.
Mishchenko, A. S.: Local Combinatorial Hirzebruch Formula, International Congress ofMathematicians, Abstracts of Short Communications and Poster Sessions, Berlin, 18-27 August 1998, p. 94.
Mishchenko, A. S.: Local combinatorial Hirzebruch formula, In: International Conference Dedicated to the 90th Anniversary of L. S. Pontryagin, Abstracts, Algebra, Geometry and Topology, 31 August-6 September (1998), pp. 119-121.
Mishchenko, A. S.: Theory of almost algebraic Poincaré complexes and local combinatorial Hirzebruch formula, Preprint IHES/M/98/84 (1998).
Mishchenko, A. S.: Local combinatorial Hirzebruch formula, Trudy MIAN 224 (1999), 249-263, in Russian; English transl.: Proc. Steklov Inst. Math. 224 (1999), 1-13.
Rights and permissions
About this article
Cite this article
Mishchenko, A.S. Theory of Almost Algebraic Poincaré Complexes and Local Combinatorial Hirzebruch Formula. Acta Applicandae Mathematicae 68, 5–37 (2001). https://doi.org/10.1023/A:1012062214272
Issue Date:
DOI: https://doi.org/10.1023/A:1012062214272