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

Hegenbarth, Friedrich (author), Repovš, Dušan (author)

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

• Language: English
• Keywords: generalized manifolds, cell-like map, normal degree one map, Steenrod L-homology, Poincaré duality complex, periodic surgery spectrum L, geometric representation, L-homology classes
• Work type: Other
• Typology: 1.16 - Independent Scientific Component Part or a Chapter in a Monograph
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Author Accepted Manuscript
• Year: 2025
• Number of pages: Str. 429-436
• PID: 20.500.12556/RUL-171742
• UDC: 515.1
• COBISS.SI-ID: 244030211
• Publication date in RUL: 01.09.2025

Record is a part of a monograph

• Title: Essays on topology : dedicated to Valentin Poénaru
• Editors: Louis Funar, Athanase Papadopoulos
• Place of publishing: Cham
• Publisher: Springer
• Year: 2025
• ISBN: 978-3-031-81413-6
• COBISS.SI-ID: 244025347