Homotopical intersection theory I
نویسنده
چکیده
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 [H-Q], but our proofs are fundamentally different.
منابع مشابه
Homotopical Intersection Theory, Ii: Equivariance
This paper is a sequel to [KW]. We develop here an intersection theory for manifolds equipped with an action of a finite group. As in [KW], our approach will be homotopy theoretic, enabling us to circumvent the specter of equivariant transversality. We give applications of our theory to embedding problems, equivariant fixed point problems and the study of periodic points of self maps.
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