Manifolds with small topological complexity
Petar Pave\v{s}i\'c
TL;DR
This paper classifies closed orientable manifolds with topological complexity up to 3 by analyzing their cohomology rings and identifying specific manifolds up to homeomorphism.
Contribution
It provides a classification of manifolds with low topological complexity and determines their cohomology rings, linking algebraic invariants to geometric structures.
Findings
Classification of manifolds with topological complexity ≤ 3
Determination of cohomology rings for these manifolds
Identification of some manifolds up to homeomorphism
Abstract
We study closed orientable manifolds whose topological complexity is at most 3 and determine their cohomology rings. For some of admissible cohomology rings we are also able to identify corresponding manifolds up to homeomorphism.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Advanced Combinatorial Mathematics