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Modular law through GKM theory
Algebraic Combinatorics. 2024. Vol. 7. No. 5. P. 1433–1451.
Horiguchi T., Mikiya M., Sato T.
The solution of Shareshian-Wachs conjecture by Brosnan-Chow and Guay-Paquet tied the graded chromatic symmetric functions on indifference graphs (or unit interval graphs) and the cohomology of regular semisimple Hessenberg varieties with the dot action. A similar result holds between unicellular LLT polynomials and twins of regular semisimple Hessenberg varieties. A recent result by Abreu-Nigro enabled us to prove these results by showing the modular law for the geometrical objects, and this is indeed done by Precup-Sommers and Kiem-Lee. In this paper, we give elementary and simpler proofs to the modular law through GKM theory.
Keywords: algebraic topology
Publication based on the results of:
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В первой части рассматриваются основы теории гомотопий: клеточные пространства, фундаментальная группа, накрытия, гомотопическая теория расслоений и высшие гомотопические группы.
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It is well known that the two-parametric Todd genus and elliptic functions of level~$d$ define $n$-multiplicative Hirzebruch genera, if~$d$ divides~$n+1$.
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учебник основан на курсе лекций, прочитанном автором студентам младших курсов Независимого московского университета.
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