The Gromov-Lawson-Rosenberg Conjecture for Z/4xZ/4
Algebraic Topology
2024-08-16 v1 Differential Geometry
K-Theory and Homology
Abstract
We prove the Gromov-Lawson-Rosenberg Conjecture for the group Z/4xZ/4 by computing the connective real k-homology of the classifying space with the Adams spectral sequence and two types of detection theorems for the kernel of the alpha invariant: one based on eta-invariants, closely following work of Botvinnik-Gilkey-Stolz, and a second one based on homological methods. Along the way, we determine differentials of the Adams spectral sequence for classifying spaces involved in the computation, and we study the cap structure of the Adams spectral sequence for sub-hopf algebras of the Steenrod algebra relevant to the computation of connective real and complex k-homology.
Keywords
Cite
@article{arxiv.2408.07895,
title = {The Gromov-Lawson-Rosenberg Conjecture for Z/4xZ/4},
author = {Noe Barcenas and Luis Eduardo Garcia-Hernandez and Raphael Reinauer},
journal= {arXiv preprint arXiv:2408.07895},
year = {2024}
}