Permutation-equivariant quantum K-theory III. Lefschetz' formula on\n \M_0,n/S_n and adelic characterization

2015/08/26 by Alexander Givental, Givental, Alexander · 1 citation
Mathematics · Computer Science · #advanced mathematical theories #Topological and Geometric Data Analysis #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1508.06697

Abstract

We continue our study of the genus-0 permutation-equivariant quantum\nK-theory of the target X=pt, and completely determine the "big J-function" of\nthis theory. The computation is based on the application of Lefschetz' fixed\npoint formula to the action of S_n on \M_0,n+1. It is an\ninstance of the general "adelic characterization" (which we state at the end\nwith reference to arXiv:1106.3136) of quantum K-theory for any target X in\nterms of quantum cohomology theory. Yet, some simplifications of non-conceptual\nnature occur in this example, making it a lucid illustration to the general\ntheory.\n

Cited by

• K-theoretic quasimap wall-crossing

Related

• Permutation-equivariant quantum K-theory VII. General theory
• Permutation-equivariant quantum K-theory VIII. Explicit reconstruction
• Two reconstruction theorems in permutation equivariant quantum K-theory
• Permutation-equivariant quantum K-theory IX. Quantum Hirzebruch-Riemann-Roch in all genera
• Permutation-equivariant quantum K-theory IV. D_q-modules