p-adic J-homomorphisms and a product formula

Details p-adic J-homomorphisms and a product formula p-adic J-homomorphisms and a product formula

2011-10-26

arxiv.org/abs/1110.5851v2

Mathematics

Algebraic Topology

Added Conjecture 4.5 on alternative description of J_{F_p}, otherwise just minor edits

Scientific paper

One-point compactification turns real vector spaces into spheres. In homotopy theory, this transformation gets encoded in a map called the "real J-homomorphism". Here we define and investigate p-adic J-homomorphisms, which sort of turn p-adic vector spaces into spheres. Our main theorem is a product formula for these J-homomorphisms, saying what happens when you start with a rational vector space. This formula specializes to Hilbert's version of the quadratic reciprocity law after applying second homotopy groups.

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