Topological coHochschild homology and the homology of free loop spaces

Spanier–Whitehead duality for topological coHochschild homology

“…The $$E_2$$‐page of this spectral sequence is computed for various interesting coalgebra spectra in [23]. In [6], Bohmann, Gerhardt and Shipley use the $$\square$$‐Hopf algebra structure on the coBökstedt spectral sequence and the equivalence above to obtain homology computations for various free loop spaces generalizing earlier computations of [25]. Recently, Ayala and Francis defined factorization cohomology which generalizes coTHH for $$\mathbb {E}_n$$‐coalgebras to obtain a Poincaré duality result for factorization homology [1].…”