In this note we introduce Thorn classes of microbundles. We determine the Thorn class of the Whitney sum as the cup product of Thorn classes and state two applications ; one to Gysin sequences of Whitney sums and one to the Atiyah-Bott-Shapiro duality theorem for Thorn spaces (cf. Atiyah [2]). Thus our main result states tha t for microbundles /xi, JU2 over a compact (topological) manifold X, i...

We construct the stable (representable) homotopy category of finite orbispectra, whose objects are formal desuspensions orbi-CW-pairs by vector bundles and morphisms classes relative maps. The representable orbispectra admits a contravariant involution extending Spanier--Whitehead duality. This duality relates homotopical cobordism theories (cohomology on orbispectra) represented global Thom sp...

Combining the approach to Thom polynomials via classifying spaces of singularities with the Fulton-Lazarsfeld theory of cone classes and positive polynomials for ample vector bundles, we show that the coefficients of the Schur function expansions of the Thom polynomials of stable singularities are nonnegative with positive sum.

The existence of a good theory of Thom isomorphisms in some rational category of mixed Tate motives would permit a nice interpolation between ideas of Kontsevich on deformation quantization, and ideas of Connes and Kreimer on a Galois theory of renormalization, mediated by Deligne’s ideas on motivic Galois groups.

In this paper, we demonstrate a relation among Seiberg-Witten invariants which arises from embedded surfaces in four-manifolds whose self-intersection number is negative. These relations, together with Taubes’ basic theorems on the Seiberg-Witten invariants of symplectic manifolds, are then used to prove the Symplectic Thom Conjecture: a symplectic surface in a symplectic four-manifold is genus...

This article analyzes the interplay between symplectic geometry in dimension four and the invariants for smooth four-manifolds constructed using holomorphic triangles introduced in [18]. Specifically, we establish a non-vanishing result for the invariants of symplectic four-manifolds, which leads to new proofs of the indecomposability theorem for symplectic four-manifolds and the symplectic Tho...

We show that a triangulated motivic category admits categorical Thom isomorphisms for vector bundles with an additional structure if and only the generalized cohomology theory represented by tensor unit object classes. also stable $\mathbb{A}^1$-derived does not admit oriented and, more generally, symplectic bundles. In order to do so we compute first homology sheaves of sphere spectrum class i...

Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincaré Duality and the Dold-Thom Theorem to establish existence of Nash Equilibria under fairly general topological hypotheses. The Dold-Thom Theorem provides us ...

Abstract We give the definition of Thom condition and we show that given any germ complex analytic function $$f:(X,x)\rightarrow ({\mathbb {C}},0)$$ f : ( X , x ) → C ...