Homology rigidity of Grassmannians
Fang Li, Haibao Duan
TL;DR
This paper extends homology rigidity results from classical to exceptional Grassmannians using Gröbner basis methods on their cohomology presentations.
Contribution
It introduces a novel application of Gröbner basis techniques to prove homology rigidity for exceptional Grassmannians.
Findings
Homology rigidity holds for all studied Grassmannians.
Gröbner basis methods effectively analyze cohomology presentations.
Extension of classical results to exceptional cases achieved.
Abstract
Applying the theory of Gr\"{o}bner basis to the Schubert presentation of the cohomology of Grassmannians, we extend the homology rigidity results known for the classical Grassmannians to the exceptional cases.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models