Lower bounds for topological complexity
Aleksandra Franc, Petar Pave\v{s}i\'c
TL;DR
This paper introduces new fibrewise definitions of monoidal topological complexity and proposes improved lower bounds that surpass traditional cohomology-based estimates, analyzing their interrelations.
Contribution
It presents novel fibrewise approaches to topological complexity and develops enhanced lower bounds that refine existing cohomological estimates.
Findings
New fibrewise Whitehead and Ganea definitions introduced
Enhanced lower bounds for topological complexity established
Relationships between different bounds analyzed
Abstract
We introduce fibrewise Whitehead- and fibrewise Ganea definitions of monoidal topological complexity. We then define several lower bounds for the topological complexity, which improve on the standard lower bound in terms of nilpotency of the cohomology ring. The relationships between these lower bounds are studied.
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