67 papers
This paper establishes averaging formulas for the Reidemeister trace, Lefschetz, and Nielsen numbers of -valued maps on closed manifolds by expressing them through single-valued maps on finite orientable covering spaces, with explicit results derived for infra-nilmanifolds.
This paper establishes an averaging formula to compute the Nielsen number of any -valued affine map on an infra-nilmanifold, extending previous results known for single-valued maps and -valued maps on nilmanifolds.
This paper constructs non-affine -valued maps on -dimensional tori (for ) that are not homotopic to affine maps, a result that contrasts sharply with the single-valued case and is achieved by establishing necessary and sufficient algebraic conditions on induced morphisms.
PTOPOFL is a privacy-preserving personalized federated learning framework that replaces gradient sharing with compact persistent homology descriptors to simultaneously mitigate data-reconstruction risks and improve aggregation performance on non-IID data through topology-guided clustering and weighted aggregation.
This paper establishes a homology theory for ample groupoids using compactly supported Moore complexes, proving functoriality and Kakutani invariance, deriving Mayer-Vietoris sequences, and demonstrating that a universal coefficient theorem holds for discrete coefficients while identifying specific obstructions for non-discrete ones.
This paper develops a theory of quantum cellular automata over arbitrary commutative rings and uses algebraic K-theory to construct a spectrum that classifies these automata up to quantum circuits and stabilization, revealing a deep connection between their classification on Euclidean lattices and the K-theory of Azumaya algebras.
This paper establishes that the newly introduced string tangential structure satisfies the condition for type IIA string theory, extends the orientation of to include level structures , and applies the resulting homotopy groups to analyze anomaly cancellation in specific string compactifications.