English

The degrees of maps between $(2n-1)$-Poincar\' e complexes

Algebraic Topology 2013-09-06 v1 Geometric Topology

Abstract

In this paper, using exclusively homotopy theoretical methods, we study degrees of maps between (n2)(n-2)-connected (2n1)(2n-1)-dimensional Poincar\' e complexes which have torsion free integral homology. Necessary and sufficient algebraic conditions for the existence of map degrees between such Poincar\' e complexes are established. We calculate the set of all map degrees between certain two (n2)(n-2)-connected (2n1)(2n-1)-dimensional torsion free Poincar\'e complexes. For low nn, using knowledge of possible degrees of self maps, we classify, up to homotopy, torsion free (n2)(n-2)-connected (2n1)(2n-1)-dimensional Poincar\' e complexes.

Cite

@article{arxiv.1309.1361,
  title  = {The degrees of maps between $(2n-1)$-Poincar\' e complexes},
  author = {Jelena Grbic and Aleksandar Vucic},
  journal= {arXiv preprint arXiv:1309.1361},
  year   = {2013}
}
R2 v1 2026-06-22T01:21:29.828Z