We formulate the notion of an isomorphism of GKM graphs. We then show that two GKM graphs have isomorphic graph equivariant cohomology algebras if and only if the graphs are isomorphic.
References
M. Franz and V. Puppe, Exact cohomology sequences with integral coefficients for torus actions, Transform. Groups 12 (2007), no. 1, 65–76. MR2308029 1420.55016 10.1007/s00031-005-1127-0M. Franz and V. Puppe, Exact cohomology sequences with integral coefficients for torus actions, Transform. Groups 12 (2007), no. 1, 65–76. MR2308029 1420.55016 10.1007/s00031-005-1127-0
M. Franz and V. Puppe, Exact sequences for equivariantly formal spaces, C. R. Math. Acad. Sci. Soc. R. Can. 33 (2011), no. 1, 1–10. MR2790824 1223.55003M. Franz and V. Puppe, Exact sequences for equivariantly formal spaces, C. R. Math. Acad. Sci. Soc. R. Can. 33 (2011), no. 1, 1–10. MR2790824 1223.55003
M. Goresky, R. Kottwitz and R. MacPherson, Equivariant cohomology, Koszul duality, and the localization theorem, Invent. Math. 131 (1998), no. 1, 25–83. MR1489894 0897.22009 10.1007/s002220050197M. Goresky, R. Kottwitz and R. MacPherson, Equivariant cohomology, Koszul duality, and the localization theorem, Invent. Math. 131 (1998), no. 1, 25–83. MR1489894 0897.22009 10.1007/s002220050197
V. Guillemin and C. Zara, Equivariant de Rham theory and graphs, Asian J. Math. 3 (1999), no. 1, 49–76. 0971.58001 10.4310/AJM.1999.v3.n1.a3V. Guillemin and C. Zara, Equivariant de Rham theory and graphs, Asian J. Math. 3 (1999), no. 1, 49–76. 0971.58001 10.4310/AJM.1999.v3.n1.a3
H. Maeda, M. Masuda and T. Panov, Torus graphs and simplicial posets, Adv. Math. 212 (2007), no. 2, 458–483. 1119.55004 10.1016/j.aim.2006.10.011H. Maeda, M. Masuda and T. Panov, Torus graphs and simplicial posets, Adv. Math. 212 (2007), no. 2, 458–483. 1119.55004 10.1016/j.aim.2006.10.011
M. Masuda, Equivariant cohomology distinguishes toric manifolds, Adv. Math. 218 (2008), no. 6, 2005–2012. 1152.57032 10.1016/j.aim.2008.04.002M. Masuda, Equivariant cohomology distinguishes toric manifolds, Adv. Math. 218 (2008), no. 6, 2005–2012. 1152.57032 10.1016/j.aim.2008.04.002
M. Masuda and T. Panov, On the cohomology of torus manifolds, Osaka J. Math. 43 (2006), no. 3, 711–746. 1111.57019 euclid.ojm/1159190010M. Masuda and T. Panov, On the cohomology of torus manifolds, Osaka J. Math. 43 (2006), no. 3, 711–746. 1111.57019 euclid.ojm/1159190010
