We obtain a combinatorial formula for the Miller-Morita-Mumford classes for the mapping class group of punctured surfaces and prove Witten's conjecture that they are proportional to the dual to the Witten cycles. The proportionality constant is shown to be exactly as conjectured by Arbarello and Cornalba [J. Alg. Geom.…
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15 results for “Miller-Morita-Mumford”
Study K3 manifold bundles proving Miller--Morita--Mumford classes non-zero.
problem Proving non-zero characteristic classes for K3 manifold bundles.
method Two methods: Franke's stable cohomology result and Miller--Morita--Mumford classes.
result Proves non-zero characteristic classes for certain bundles.
Study on smooth bundles with nonpositive curvature, proving vanishing classes and rigidity.
problem Characterizing smooth bundles with nonpositive curvature fibers.
method Proving vanishing results for Miller-Morita-Mumford classes and showing topological rigidity.
result Vanishing of generalized Miller-Morita-Mumford classes and topological rigidity of vertical tangent bundles.
Kappa classes on KSBA spacesmath.AG
Defines kappa classes on KSBA spaces, generalizing classes on curves.
problem Generalizing Miller-Morita-Mumford classes to KSBA stable varieties and pairs.
method Defining kappa classes on KSBA moduli spaces and computing them in specific cases.
result Computed kappa classes on Campedelli surfaces, including finding the Chow ring of a specific GIT quotient.
Study characteristic classes for manifold bundles, focusing on fiber families.
problem Understanding characteristic classes for families of bundles.
method Construction of relative Sullivan models and explicit cocycle representatives for characteristic classes.
result Tools for computing the rational cohomology ring of and subring of generalized Miller-Morita-Mumford classes.
Vanishing theorem for tautological classes on aspherical manifolds.
problem Understanding rational cohomology of classifying spaces for diffeomorphism groups.
method Using tautological classes and rational cohomology to show vanishing for aspherical manifolds.
result Rational tautological classes depend only on the underlying topological block bundle, leading to vanishing results.
Using certain Thom spectra appearing in the study of cobordism categories, we show that the odd half of the Miller-Morita-Mumford classes on the mappping class group of a surface with negative Euler characteristic vanish in integral cohomology when restricted to the handlebody subgroup. This is a special case of a more…
New configuration space integrals show nontrivial formal smooth structures on 4-manifold bundles.
problem Disproving the 4-dimensional Smale conjecture by constructing nontrivial bundles.
method Defining new configuration space integrals relying on formal smooth structures.
result Discovering a generalized Miller-Morita-Mumford class obstructing formal smooth structures.
This paper attempts to investigate the space of various characteristic classes for smooth manifold bundles with local system on the total space inducing a finite holonomy covering. These classes are known as twisted higher torsion classes. We will give a system of axioms that we require these cohomology classes to sati…
Diagonalizes tautological classes of definite 4-manifolds.
problem Diagonalizing tautological classes of definite 4-manifolds.
method Families version of Bauer-Furuta cohomotopy refinement of Seiberg-Witten theory.
result Completely determined tautological rings of and .
Study bundles over surfaces with specific fibers, determining characteristic numbers and obstructions.
problem Characterizing bundles over surfaces with highly connected fibers.
method Analyzing smooth and topological bundles, providing necessary and sufficient conditions, and computing characteristic numbers.
result Determine characteristic numbers and divisibility constraints on signatures and genera for bundles of this type.
We revisit three results due to Morita expressing certain natural integral cohomology classes on the universal family of Riemann surfaces C_g, coming from the parallel symplectic form on the universal jacobian, in terms of the Miller-Morita-Mumford classes e and e_1. Our discussion will be on the level of the natural 2…
Characteristic classes of oriented vector bundles can be identified with cohomology classes of the disjoint union of classifying spaces BSO_n of special orthogonal groups SO_n with n=0,1,... A characteristic class is stable if it extends to a cohomology class of a homotopy colimit BSO of classifying spaces BSO_n. Simil…
A singular point of a smooth map F: M -> N of manifolds is a point in M at which the rank of the differential dF is less than the minimum of dimensions of M and N. The classical invariant of the set S of singular points of F of a given type is defined by taking the fundamental class [\bar{S}]\in H_*(M) of the closure o…
Torelli groups' homology is finitely generated in stable range.
problem Whether the homology groups of Torelli subgroups are finitely generated in stable range.
method Using unipotency condition and Tavgen's theorem.
result Homology groups are finitely generated in stable range.