A persistence Spanier-Whitehead category of filtered CW complexes is defined, proven to be a triangulated persistence category, and its K-group is shown to be isomorphic to the Novikov polynomial ring via the weighted Euler characteristic.
Triangulation, Persistence, and Fukaya categories
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abstract
This paper introduces a new algebraic notion - triangulated persistence category (TPC) - that refines that of triangulated category in the same sense that a persistence module is a refinement of the notion of a vector space. The spaces of morphisms of such a TPC are persistence modules and this category is endowed with a class of weighted distinguished triangles. Under favourable conditions we show that the derived Fukaya category admits a TPC refinement and this is applied to deduce a global rigidity result for spaces of compact, exact Lagrangians in certain Liouville manifolds: we construct a metric on this space with intrinsic symplectic properties.
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Filtered Topology and Persistence in Stable Homotopy
A persistence Spanier-Whitehead category of filtered CW complexes is defined, proven to be a triangulated persistence category, and its K-group is shown to be isomorphic to the Novikov polynomial ring via the weighted Euler characteristic.