At Studio A, a supported studio for neurodiverse artists, the prolific painter, performer, photocopier, and installation artist Thom Roberts frequently reaches out to connect with friends fellow artists by running his hands across backs of their heads; “reading” crowns. It’s blessing I have been lucky enough receive countless times over course my ethnographic engagement as relationship has deve...

By results of Löffler and Comezaña, the Pontrjagin-Thom map from geometric G-equivariant bordism to homotopy theoretic equivariant bordism is injective for compact abelian G. If G = S×. . .×S, we prove that the associated fixed point square is a pull back square, thus confirming a recent conjecture of Sinha [22]. This is used in order to determine the image of the Pontrjagin-Thom map for toral G.

The classical Thom–Porteous formula expresses the homology class of the degeneracy locus of a generic map between two vector bundles as an alternating sum of Schur polynomials. A proof of this formula was given by Pragacz by expressing this alternating sum as the Euler characteristic of a Schur complex, which gives an explanation for the signs. Fulton later generalized this formula to the situa...

In this paper we present a way of computing a lower bound for genus of any smooth representative of a homology class of positive self-intersection in a smooth four-manifold X with second positive Betti number b+2 (X) = 1. We study the solutions of the Seiberg-Witten equations on the cylindrical end manifold which is the complement of the surface representing the class. The result can be formula...

Using geometric homology and cohomology we give a simple conceptual proof of the Thom isomorphism theorem.

R. Rimányi defined the incidence class of two singularities η and ξ as [η]|ξ, the restriction of the Thom polynomial of η to ξ. He conjectured that (under mild conditions) [η]|ξ 6= 0 ⇐⇒ ξ ⊂ η. Generalizing this notion we define the incidence class of two orbits η and ξ of a representation. We give a sufficient condition (positivity) for ξ to have the property that [η]|ξ 6= 0 ⇐⇒ ξ ⊂ η for any ot...

This paper is on the homotopy classification of maps of (n+1)-dimensional manifolds into the n-dimensional sphere. For a continuous map f : M → S define the degree deg f ∈ H1(M;Z) to be the class dual to f[S], where [S] ∈ H(S;Z) is the fundamental class. We present a short and direct proof of the following specific case of the Pontryagin-Steenrod-Wu theorem: Theorem. Let M be a connected orient...