18 papers
This paper computes the derived Witt groups of smooth proper curves over nondyadic local fields of characteristic not equal to 2 by utilizing reduction techniques and conducting a general study of the existence of Theta characteristics.
This paper reformulates the Chern character in topological K-theory using Fermi points of Fredholm operators to generalize spectral flow and provide elementary proofs for the evenness of the edge index and the bulk-edge correspondence in four-dimensional time-reversal symmetric topological insulators (class AI).
This paper investigates homotopy decompositions of classifying spaces of compact connected Lie groups via a relative fiber-cofiber construction, establishing rational sharpness and Cohen-Macaulay properties for the resulting spaces under specific cohomological conditions while providing explicit cohomological and K-theoretic computations for examples involving maximal tori and commuting elements.
This paper constructs a smooth projective complex surface with a representable Chow group of 0-cycles that lacks a universal 0-cycle, thereby providing a two-dimensional analogue to Voisin's counterexample and yielding the first known instance of a smooth projective threefold of Kodaira dimension zero with a non-torsion, non-algebraic Hodge class of degree 4.
This paper constructs smooth affine algebras of dimension over an algebraically closed field of characteristic zero that admit nontrivial projective modules of rank with trivial total Chern classes, thereby demonstrating the existence of nontrivial vector bundles whose topological invariants vanish.
This paper investigates equivalent characterizations of totally acyclicity for acyclic complexes of projective, injective, and flat modules over arbitrary rings, linking these conditions to homological invariants like silp(R), spli(R), and sfli(R) while refining existing results on the equality of these invariants and extending characterizations of Iwanaga-Gorenstein rings and the Nakayama conjecture to the non-commutative setting.
This paper investigates the robustness of topological phases on aperiodic lattices by constructing *-homomorphisms between groupoid and coarse-geometric models, demonstrating that strong phases are detected by position spectral triples while phases arising from stacking along Delone sets are inherently weak in the coarse-geometric sense.
This paper computes specific Ext and Tor groups for general functors from a -linear additive category to vector spaces by relating them to the corresponding groups for additive functors, thereby providing new methods for calculating the group homology of general linear groups.
This paper establishes the theorem of the heart for Weibel's homotopy -theory (), proving that the realization functor induces an equivalence for small stable -categories with bounded -structures, a result derived from a strengthened version of Barwick's theorem that provides precise isomorphism ranges for classical -theory and demonstrates the sharpness of these bounds.
This paper clarifies that the invariance of -theory under duality is a purely formal property, contrasting it with the non-formal nature of the general statement for arbitrary localizing invariants, and provides a counterexample to the claim that the universal localizing invariant is invariant under taking opposite categories.
This paper establishes the foundational theory of covers and envelopes within proto-exact categories and applies these results to prove that categories of Banach modules over arbitrary Banach rings possess enough injectives.
This paper establishes a groupoid-equivariant formulation of the Fredholm index by constructing a natural KK-theory class for Fredholm operators within the unitary conjugation groupoid framework, demonstrating that its composition with the Calkin extension boundary map recovers the classical index.
This paper constructs a spectral sequence converging to operadic tangent cohomology by utilizing filtrations from towers of cofibrations, thereby providing new algebraic descriptions of the Serre spectral sequence and the rational homotopy groups of self-fiber-homotopy equivalences.
This paper proves that for a specific class of Koras-Russell threefolds defined over an algebraically closed field of characteristic zero, the Chow groups are trivial, implying that all algebraic vector bundles over these varieties are trivial, with the additional result that their Chow-Witt groups are also trivial when a specific parameter is odd.
This paper demonstrates that quantum cellular automata constitute the degree-zero component of a coarse homology theory, thereby providing a formal framework that explains why the space of such automata forms an Omega-spectrum.
This paper proves that the Hochschild cohomology ring of any self-injective Nakayama algebra is a Batalin-Vilkovisky algebra, thereby demonstrating that the semisimplicity condition on the Nakayama automorphism required in previous results is not necessary, while also correcting inaccuracies found in existing literature.
This paper establishes homological stability for automorphisms of symmetric bilinear forms over a broad class of principal ideal domains, thereby determining a significant portion of the stable cohomology of odd orthogonal groups over the integers in low degrees.
This paper refines the string equation on from the Chow ring to algebraic cobordism to derive inductive formulas for cobordism-valued psi-class intersections and explicit classes up to , including their images in -theory.