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Creators/Authors contains: "Weng, Daping"

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  1. ; ; (, Transactions of the American Mathematical Society)
    We introduce a topological intersection number for an ordered pair of SL 3 \operatorname {SL}_3 -webs on a decorated surface. Using this intersection pairing between reduced ( SL 3 , A ) (\operatorname {SL}_3,\mathcal {A}) -webs and a collection of ( SL 3 , X ) (\operatorname {SL}_3,\mathcal {X}) -webs associated with the Fock–Goncharov cluster coordinates, we provide a natural combinatorial interpretation of the bijection from the set of reduced ( SL 3 , A ) (\operatorname {SL}_3,\mathcal {A}) -webs to the tropical set A PGL 3 , S ^<#comment/> + ( Z t ) \mathcal {A}^+_{\operatorname {PGL}_3,\hat {S}}(\mathbb {Z}^t) , as established by Douglas and Sun in [Forum Math. Sigma 12 (2024), p. e5, 55]. We provide a new proof of the flip equivariance of the above bijection, which is crucial for proving the Fock–Goncharov duality conjecture of higher Teichmüller spaces for SL 3 \operatorname {SL}_3 . 
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    Free, publicly-accessible full text available August 1, 2026
  2. ; ; (, Geometric and Functional Analysis)
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