TY - JOUR
T1 - On the bounded index property for products of aspherical polyhedra
AU - Zhang, Qiang
AU - Ye, Shengkui
N1 - Publisher Copyright:
© 2020 Juliusz Shauder Centre for Nonlinear Studies Niolaus Copernius University in Toruń.
PY - 2020
Y1 - 2020
N2 - A compact polyhedron X is said to have the Bounded Index Property for Homotopy Equivalences (BIPHE) if there is a finite bound B such that for any homotopy equivalence f: X → X and any fixed point class F of f, the index |ind(f, F)| ≤ B. In this note, we consider the product of compact polyhedra, and give some sufficient conditions for it to have BIPHE. Moreover, we show that products of closed Riemannian manifolds with negative sectional curvature, in particular hyperbolic manifolds, have BIPHE, which gives an affirmative answer to a special case of a question asked by Boju Jiang.
AB - A compact polyhedron X is said to have the Bounded Index Property for Homotopy Equivalences (BIPHE) if there is a finite bound B such that for any homotopy equivalence f: X → X and any fixed point class F of f, the index |ind(f, F)| ≤ B. In this note, we consider the product of compact polyhedra, and give some sufficient conditions for it to have BIPHE. Moreover, we show that products of closed Riemannian manifolds with negative sectional curvature, in particular hyperbolic manifolds, have BIPHE, which gives an affirmative answer to a special case of a question asked by Boju Jiang.
KW - Aspherical polyhedron
KW - Bounded index property
KW - Fixed point
KW - Negative curved manifold
KW - Product
UR - http://www.scopus.com/inward/record.url?scp=85101611103&partnerID=8YFLogxK
U2 - 10.12775/TMNA.2019.116
DO - 10.12775/TMNA.2019.116
M3 - Article
AN - SCOPUS:85101611103
SN - 1230-3429
VL - 56
SP - 419
EP - 432
JO - Topological Methods in Nonlinear Analysis
JF - Topological Methods in Nonlinear Analysis
IS - 2
ER -