English

Nonabelian Poincare duality after stabilizing

Algebraic Topology 2013-05-20 v4

Abstract

We generalize the nonabelian Poincare duality theorems of Salvatore in [Sal01] and Lurie in [Lur09] to the case of not necessarily grouplike E_n-algebras (in the category of spaces). We define a stabilization procedure based on McDuff's "brining points in from infinity" maps from [McD75]. For open connected parallelizable n-manifolds, we prove that, after stabilizing, the topological chiral homology of M with coefficients in an E_n-algebra A, is homology equivalent to Map^c(M,B^n A), the space of compactly supported maps to the n-fold classifying space of A. The two models of topological chiral homology used in this paper are Andrade's model from [And10] and Salvatore's from [Sal01].

Keywords

Cite

@article{arxiv.1209.2773,
  title  = {Nonabelian Poincare duality after stabilizing},
  author = {Jeremy Miller},
  journal= {arXiv preprint arXiv:1209.2773},
  year   = {2013}
}

Comments

33 pages, 5 figures. arXiv admin note: text overlap with arXiv:1210.7377

R2 v1 2026-06-21T22:04:09.187Z