Morse complexes of compact Lie monoids are equipped with f-bialgebra structures that define infinity-functors, extending to closed manifolds and manifolds with compact Lie group actions.
Continuous and coherent actions on wrapped Fukaya categories.arXiv:1911.00349
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Using Floer theory on Hamiltonian bundles, the paper constructs natural homomorphisms from π_m(BG) to categorified K-theory groups K^Cat_m(R) and gives a geometric proof that K^Cat_2(Z) is infinitely generated.
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The Morse complex is an $\infty$-functor
Morse complexes of compact Lie monoids are equipped with f-bialgebra structures that define infinity-functors, extending to closed manifolds and manifolds with compact Lie group actions.
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Hamiltonian elements in algebraic K-theory
Using Floer theory on Hamiltonian bundles, the paper constructs natural homomorphisms from π_m(BG) to categorified K-theory groups K^Cat_m(R) and gives a geometric proof that K^Cat_2(Z) is infinitely generated.