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Abstract

In this paper, we characterize the set of all Betti sequences of compact triangulable homology manifolds. In addition, we characterize the Betti sequences of all Buchsbaum-Eulerian, Eulerian, and semi-Eulerian complexes, and the depths of their Stanley-Reisner rings.

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References

  1. A. Björner and T. Hibi, “Betti Numbers of Buchsbaum Complexes”, Math. Scand. 67 (1990), 193–196.

    MathSciNet  MATH  Google Scholar 

  2. C. Chan, D. Jungreis, and R. Stong, “Buchsbaum and Eulerian Complexes” (1993), J. Pure & Applied Algebra, to appear.

    Google Scholar 

  3. M. Greenberg and J. Harper, “Algebraic Topology: A First Course” (1981), Beniamin/Cummings, Reading, Mass.

    MATH  Google Scholar 

  4. T. Hibi, “Quotient Algebras of Stanley-Reisner Rings and Local Cohomology”, J. Algebra 140 2 (1991), 336–343.

    Article  MathSciNet  MATH  Google Scholar 

  5. T. Hibi, “Hochster’s Formula on Betti Numbers and Buchsbaum Complexes”, preprint (1993).

    Google Scholar 

  6. F. Hirzebruch, “Topological Methods in Algebraic Geometry” (1978), Springer-Verlag, New York.

    MATH  Google Scholar 

  7. M. Miyazaki, “Characterizations of Buchsbaum complexes”, Manuscripta Math. 63 (1989), 245–254.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Munkres, “Topological Results in Combinatorics”, Michigan Math. J. 31 (1984), 113–128.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Munkres “Algebraic Topology” (1984). Addison-Wesley, Menlo-Park, CA.

    MATH  Google Scholar 

  10. G. Reisner, “Cohen-Macaulay quotients of polynomial rings”, Adv. in Math. 21 (1976), 30–49.

    Article  MathSciNet  MATH  Google Scholar 

  11. P. Schenzel, “On the number of faces of simplicial complexes and the purity of Frobenius”, Math. Z.178 (1981), 125–142.

    Article  MathSciNet  MATH  Google Scholar 

  12. E. Snanier. “Algebraic Topology” (1966), McGraw-Hill, Inc., New York.

    Google Scholar 

  13. R. Stanley, “Combinatorics and Commutative Algebra”, Prog. in Math. 41 (1983), Birkhäuser, Boston /Basel /Stuttgart.

    MATH  Google Scholar 

  14. R. Stanley, “Enumerative Combinatorics” 1 (1986), Wadsworth, Brooks, & Cole, Pacific Grove.

    MATH  Google Scholar 

  15. R. Stanley, “A Survey of Eulerian Posets”, Polytopes: Abstract, Convex, and Computational (T. Bisztriczky, P. McMullen, R. Schneider, A. I. Weiss, eds.), NATO ASI Series C 440 (1994), Kluwer Academic Publishers.

    Google Scholar 

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© 1995 Springer Science+Business Media Dordrecht

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Chan, C.S., Jungreis, D., Stong, R. (1995). Depths and Betti Numbers of Homology Manifolds. In: White, N.L. (eds) Invariant Methods in Discrete and Computational Geometry. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8402-9_16

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  • DOI: https://doi.org/10.1007/978-94-015-8402-9_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4572-0

  • Online ISBN: 978-94-015-8402-9

  • eBook Packages: Springer Book Archive

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