Related papers: Fiberwise Intersection Theory
We define an invariant for the existence of r pointwise linearly independent sections in the tangent bundle of a closed manifold. For low values of r, explicit computations of the homotopy groups of certain Thom spectra combined with…
This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the…
We use topological quantum field theory to derive an invariant of a three-manifold with boundary. We then show how to use this invariant as an obstruction to embedding one three-manifold in another.
Many examples of obstruction theory can be formulated as the study of when a lift exists in a commutative square. Typically, one of the maps is a cofibration of some sort and the opposite map is a fibration, and there is a functorial…
Within its traditional range of perversity parameters, intersection cohomology is a topological invariant of pseudomanifolds. This is no longer true once one allows superperversities, in which case intersection cohomology may depend on the…
We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surface braids and surface links, we also define an invariant that…
We give a new definition of an obstruction theory for infinitesimal deformation theory and relate it to earlier definitions of Artin, Fantechi-Manetti, Li-Tian, and Behrend-Fantechi.
Coincidences of maps between smooth manifolds are studied via a geometric approach which involves (nonstabilized) normal bordism theory and pathspaces.
We give an obstruction for lifts and extensions in a model category inspired by Klein and Williams' work on intersection theory. In contrast to the familiar obstructions from algebraic topology, this approach produces a single invariant…
We study the obstruction to the exactness of the variational complex for a field theory on an affine bundle.
We develop an obstruction theory for Hirsch extensions of cbba's with twisted coefficients. This leads to a variety of applications, including a structural theorem for minimal cbba's, a construction of relative minimal models with twisted…
In a diffeomorphism invariant theory, symmetry breaking may be a mask for coordinate choice.
We provide a necessary and sufficient condition for the derived self-intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme. As a consequence we deduce a generalized HKR isomorphism. We also…
When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers…
We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.
We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this…
Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a…
We construct geometric examples of pseudomanifolds that satisfy the Witt condition for intersection homology Poincare duality with respect to certain fields but not others. We also compute the bordism theory of $K$-Witt spaces for an…
Given a map f: M \to M of closed topological manifolds we define torsion obstructions whose vanishing is a necessary condition for f being homotopy equivalent to a projection of a locally trivial fiber bundle. If N = S^1, these torsion…
We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.