On geometric representation of ${\mathbb L}$-homology classes

Hegenbarth, Friedrich (avtor), Repovš, Dušan (avtor)

In 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 $\Gamma: H_n(B;{\mathbb L}) \longrightarrow {\mathcal N}^{H}_{n}(B,\partial)$.

• Jezik: Angleški jezik
• Ključne besede: generalized manifolds, cell-like map, normal degree one map, Steenrod L-homology, Poincaré duality complex, periodic surgery spectrum L, geometric representation, L-homology classes
• Vrsta gradiva: Drugo
• Tipologija: 1.16 - Samostojni znanstveni sestavek ali poglavje v monografski publikaciji
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Recenzirani rokopis
• Leto izida: 2025
• Št. strani: Str. 429-436
• PID: 20.500.12556/RUL-171742
• UDK: 515.1
• COBISS.SI-ID: 244030211
• Datum objave v RUL: 01.09.2025

Gradivo je del monografije

• Naslov: Essays on topology : dedicated to Valentin Poénaru
• Uredniki: Louis Funar, Athanase Papadopoulos
• Kraj izida: Cham
• Založnik: Springer
• Leto izida: 2025
• ISBN: 978-3-031-81413-6
• COBISS.SI-ID: 244025347