On geometric representation of ${\mathbb L}$-homology classesHegenbarth, Friedrich (Avtor) Repovš, Dušan (Avtor) generalized manifoldscell-like mapnormal degree one mapSteenrod L-homologyPoincaré duality complexperiodic surgery spectrum Lgeometric representationL-homology classesIn this chapter we give a geometric representation of $H_{n}(B;{\mathbb L})$ classes, where ${\mathbb L}$ is the $4$-periodic surgery spectrum, by establishing a relationship between the normal cobordism classes ${{\mathcal N}}^{H}_{n}(B,\partial)$ and the $n$-th ${\mathbb L}$-homology of $B$, representing the elements of $H_{n}(B;{\mathbb L})$ by normal degree one maps with a reference map to $B$. More precisely, we prove that for every $n \ge 6$ and every finite complex $B$, there exists a map $\Gamma: H_n(B;{\mathbb L}) \longrightarrow {\mathcal N}^{H}_{n}(B,\partial)$.20252025-09-01 12:16:31Neznano171742sl