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Coxeter cochain complexes

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Abstract

We define the Coxeter cochain complex of a Coxeter group (G, S) with coefficients in a ℤ[G]-module A. This is closely related to the complex of simplicial cochains on the abstract simplicial complex I(S) of the commuting subsets of S. We give some representative computations of Coxeter cohomology and explain the connection between the Coxeter cohomology for groups of type A, the (singular) homology of certain configuration spaces, and the (Tor) homology of certain local Artin rings.

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References

  1. M. Adamaszek and J. Barmak, On a lower bound for the connectivity of the independence complex of a graph, Discrete mathematics 311 (2011), 2566–2569.

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Bousquet-Mélou, S. Linusson and E. Nevo, On the independence complex of square grids, Journal of Algebraic Combinatorics 27 (2008), 423–450.

    Article  MATH  Google Scholar 

  3. R. Ehrenborg and G. Hetyei, The topology of the independence complex, European Journal of Combinatorics 27 (2006), 906–923.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Engström, Independence complexes of claw-free graphs, European Journal of Combinatorics 28 (2008), 234–241.

    Article  Google Scholar 

  5. J. Jonsson, Certain Homology Cycles of the Independence Complex of Grids, Discrete & Computational Geometry 43 (2010), 927–950.

    Article  MATH  MathSciNet  Google Scholar 

  6. D. N. Kozlov, A class of hypergraph arrangements with shellable intersection lattice, Journal of Combinatorial Theory, Series A 86 (1999), 169–176.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Lindenstrauss, The Hochschild homology of fatpoints, Israel Journal of Mathematics 133 (2003), 177–188.

    Article  MATH  MathSciNet  Google Scholar 

  8. I. Peeva, V. Reiner and V. Welker, Cohomology of real diagonal subspace arrangements via resolutions, Compositio Mathematica 117 (1999), 99–115.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA

    Michael Larsen & Ayelet Lindenstrauss

Authors
  1. Michael Larsen
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  2. Ayelet Lindenstrauss
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Correspondence to Michael Larsen.

Additional information

Michael Larsen was partially supported by NSF grant DMS-1101424.

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Larsen, M., Lindenstrauss, A. Coxeter cochain complexes. Isr. J. Math. 203, 173–187 (2014). https://doi.org/10.1007/s11856-014-0034-2

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  • DOI: https://doi.org/10.1007/s11856-014-0034-2

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