We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of Thom polynomials of Lagrange singularities have always nonnegative coefficients. This is an analog of a result on Thom polynomials of mapping singularities and Sch...

The motivation for this definition is to give in K-theory a satisfactory Thom isomorphism and Poincaré duality pairing which are analogous to the usual ones in cohomology with local coefficients. More precisely, as proved in [K1] (a precursor to twisted K-theory), if V is a real vector bundle on a compact space X with a positive metric, the K-theory of the Thom space of V is isomorphic to a cer...

Two tickets from each class advanced from yesterday’s class e lec­ tion prim aries to tom orrow ’s runoffs w ith what Tom Koegel, O m ­ budsm an election chairman, term ed "a phenom enal turnout, the best in years ” The tickets headed by presidential candidates Tom Lupo and Tom Schuler received 227 votes (2 3 p e rc e n t) and 216 votes (21 .8 p e r­ cent), respectively, to earn spots in the se...

LetG be a compact Lie group. LetM be a smoothG-manifold and V → M be an oriented G-equivariant vector bundle. One defines the spaces of equivariant forms with generalized coefficients on V and M . An equivariant Thom form θ on V is a compactly supported closed equivariant form such that its integral along the fibres is the constant function 1 on M . Such a Thom form was constructed by Mathai an...

We investigate an equivariant generalization of Morse theory for a general class of integrable models. In particular, we derive equivariant versions of the classical Poincaré-Hopf and Gauss-Bonnet-Chern theorems and present the corresponding path integral generalizations. Our approach is based on equivariant cohomology and localization techniques, and is closely related to the formalism develop...

We prove that the homology of the mapping class groups of non-orientable surfaces stabilizes with the genus of the surface. Combining our result with recent work of Madsen and Weiss, we obtain that the classifying space of the stable mapping class group of non-orientable surfaces, up to homology isomorphism, is the infinite loop space of a Thom spectrum built from the canonical bundle over the ...

The existence of a corank one map of negative codimension puts strong restrictions on the topology of the source manifold. It implies many vanishing theorems on characteristic classes and often even vanishing of the cobordism class of the source manifold. Most of our results lie deeper than just vanishing of Thom polynomials of the higher singularities. We blow up the singular map along the sin...

In this paper, we discuss elliptic genera of (2,2) and (0,2) supersymmetric Landau-Ginzburg models over nontrivial spaces, i.e. nonlinear sigma models on nontrivial noncompact manifolds with superpotential, generalizing old computations in Landau-Ginzburg models over (orbifolds of) vector spaces. For Landau-Ginzburg models in the same universality class as nonlinear sigma models, we explicitly ...