JOURNAL ARTICLE
Homotopy type through homology groups
Andrés Carnero BravoOmar Antolín Camarena
Year: 2024 Journal: Greater South Information System
Abstract
Abstract We show that for certain pairs of nonnegative integers, if the reduced integral homology groups of a space are nonzero only in that pair of degrees and those groups are finitely generated free abelian groups, then the space must have the weak homotopy type of a wedge of spheres of whose dimensions belong to the pair.
Keywords:
Homotopy Homology (biology) Homotopy group Homotopy sphere Abelian group n-connected Homotopy category Bott periodicity theorem Singular homology
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Topics
Homotopy and Cohomology in Algebraic Topology
Physical Sciences → Mathematics → Mathematical Physics
Topological and Geometric Data Analysis
Physical Sciences → Computer Science → Computational Theory and Mathematics
Geometric and Algebraic Topology
Physical Sciences → Mathematics → Geometry and Topology
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JOURNAL ARTICLE
Homotopy type through homology groups
Andrés Carnero BravoOmar Antolín Camarena
Journal: Greater South Information System Year: 2024