Homotopical Intersection Theory, I

Abstract

We give a new approach to intersection theory. Our "cycles" are closed manifolds mapping into compact manifolds and our "intersections" are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn, but our proofs are fundamentally different.

References in corpus (3)

• Embedding, compression and fiberwise homotopy theory
• Toward a general theory of linking invariants
• The Moduli Space of Thickenings

Cited by in corpus (10)

• Multiple disjunction for spaces of smooth embeddings
• The van Kampen obstruction and its relatives
• A Manifold Calculus Approach to Link Maps and the Linking Number
• Relative fixed point theory
• Minimum numbers and Wecken theorems in topological coincidence theory. I
• A stable range description of the space of link maps
• Periodic points and topological restriction homology
• Graphing, homotopy groups of spheres, and spaces of long links and knots
• Homotopical Intersection Theory, III: multi-relative intersection problems
• Obstructions in a model category and Klein and Williams' intersection invariants