Year: 2011
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Clausen, Dustin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1663525908