RT Journal Article
T1 About the homological discrete Conley index of isolated invariant acyclic continua
A1 Hernández Corbato, Luis
A1 Le Calvez, Patrice
A1 Romero Ruiz del Portal, Francisco
AB This article includes an almost self-contained exposition on the discrete Conley index and its duality. We work with a locally defined homeomorphism f in R-d and an acyclic continuum X, such as a cellular set or a fixed point, invariant under f and isolated. We prove that the trace of the first discrete homological Conley index of f and X is greater than or equal to -1 and describe its periodical behavior. If equality holds then the traces of the higher homological indices are 0. In the case of orientation-reversing homeomorphisms of R-3, we obtain a characterization of the fixed point index sequence {i(f(n) (,) p}n >= 1 for a fixed point p which is isolated as an invariant set. In particular, we obtain that i(f , p) <= 1. As a corollary, we prove that there are no minimal orientation-reversing homeomorphisms in R-3.
PB Geometry & Topology Publications, Univ Warwick, Mathematics Inst
SN 1465-3060
YR 2013
FD 2013
LK https://hdl.handle.net/20.500.14352/33437
UL https://hdl.handle.net/20.500.14352/33437
NO MICINN
NO MTM
NO FPU scholarship
DS Docta Complutense
RD 7 abr 2025