Theoretical analysis reveals that higher-order Massey products compute equivariant spectral sequence differentials, indicating sharper bounds on Betti numbers for cyclic covering spaces.
Key Points
Analyze the differentials in the Papadima–Suciu equivariant spectral sequence using higher-order Massey products and establish topological bounds for cyclic covers.
Analyzed differentials within equivariant spectral sequences using higher-order algebraic Massey products over arbitrary field coefficients.
Applied algebraic topology techniques to characterize Alexander modules, rank-one local systems, and complements of hyperplane arrangements.
Demonstrated that all differentials in the Papadima–Suciu equivariant spectral sequence are computed by higher-order Massey products.
Extended Pajitnov's correspondence between Alexander module Jordan block sizes and Massey product lengths to arbitrary field coefficients, providing improved computable upper bounds on mod p Betti numbers.
Established that vanishing higher-order Massey products ensure mod p Betti numbers of prime power cyclic covers in hyperplane arrangements are combinatorially determined.