Homotopy theory of graphs
Eric Babson1
, Hélène Barcelo2
, Mark de Longueville3
and Reinhard Laubenbacher4
1University of Washington Department of Mathematics Seattle WA
2Arizona State University Department of Mathematics and Statistics Tempe Arizona 85287-1804
3Freie Universität Berlin Fachbereich Mathematik Arnimallee 3-5 D-14195 Berlin Germany
4Virginia Polytechnic Institute and State University Virginia Bioinformatics Institute Blacksburg VA 24061
2Arizona State University Department of Mathematics and Statistics Tempe Arizona 85287-1804
3Freie Universität Berlin Fachbereich Mathematik Arnimallee 3-5 D-14195 Berlin Germany
4Virginia Polytechnic Institute and State University Virginia Bioinformatics Institute Blacksburg VA 24061
DOI: 10.1007/s10801-006-9100-0
Pages: 31–44
Full Text: PDF
References
1. R. Atkin, “An algebra for patterns on a complex, I,” Internat. J. Man-Machine Stud. 6 (1974), 285- 307.
2. R. Atkin, “An algebra for patterns on a complex, II,” Internat. J. Man-Machine Stud. 8 (1976), 483- 448.
3. Héléne Barcelo and Reinhard Laubenbacher, “Perspectives on A-homotopy theory and its applications,” to appear, special Issue of Discr. Math. 298 (2002) 39-61.
4. Héléne Barcelo, Xenia Kramer, Reinhard Laubenbacher, and Christopher Weaver, “Foundations of a connectivity theory for simplicial complexes,” Adv. Appl. Math. 26 (2001), 97-128.
5. A. Bj\ddot orner, private communication.
6. A. Bj\ddot orner and V. Welker, “The homology of “k-Equal” manifolds and related partition lattices,” Adv. in Math. 110 (1995), 277-313. Springer J Algebr Comb (2006) 24:31-44
7. X. Kramer and R. Laubenbacher, “Combinatorial homotopy of simplicial complexes and complex information networks,” in “Applications of computational algebraic geometry,” D. Cox and B. Sturmfels (eds.), Proc. Sympos. in Appl. Math., vol. 53, Amer. Math. Soc., Providence, 1998.
8. P. May, Simplicial Objects in Algebraic Topology, The University of Chicago Press, Chicago, 1967.
9. V. Voevodsky, A1-homotopy theory, Doc. Math., J. DMV, Extra Vol. ICM Berlin 1998, vol. I, 579-604 (1998).
10. D. West, Introduction to Graph Theory, second edition, Prentice-Hall, Upper Saddle River, 2001.
2. R. Atkin, “An algebra for patterns on a complex, II,” Internat. J. Man-Machine Stud. 8 (1976), 483- 448.
3. Héléne Barcelo and Reinhard Laubenbacher, “Perspectives on A-homotopy theory and its applications,” to appear, special Issue of Discr. Math. 298 (2002) 39-61.
4. Héléne Barcelo, Xenia Kramer, Reinhard Laubenbacher, and Christopher Weaver, “Foundations of a connectivity theory for simplicial complexes,” Adv. Appl. Math. 26 (2001), 97-128.
5. A. Bj\ddot orner, private communication.
6. A. Bj\ddot orner and V. Welker, “The homology of “k-Equal” manifolds and related partition lattices,” Adv. in Math. 110 (1995), 277-313. Springer J Algebr Comb (2006) 24:31-44
7. X. Kramer and R. Laubenbacher, “Combinatorial homotopy of simplicial complexes and complex information networks,” in “Applications of computational algebraic geometry,” D. Cox and B. Sturmfels (eds.), Proc. Sympos. in Appl. Math., vol. 53, Amer. Math. Soc., Providence, 1998.
8. P. May, Simplicial Objects in Algebraic Topology, The University of Chicago Press, Chicago, 1967.
9. V. Voevodsky, A1-homotopy theory, Doc. Math., J. DMV, Extra Vol. ICM Berlin 1998, vol. I, 579-604 (1998).
10. D. West, Introduction to Graph Theory, second edition, Prentice-Hall, Upper Saddle River, 2001.