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  • Controlled surgery and ▫$\mathbb{L}$▫-homology
    Hegenbarth, Friedrich, 1940- ; Repovš, Dušan, 1954-
    This paper presents an alternative approach to controlled surgery obstructions. The obstruction for a degree one normal map ▫$(f,b) \colon M^n \to X^n$▫ with control map ▫$q \colon X^n \to B$▫ to ... complete controlled surgery is an element ▫$\sigma^c (f,b) \in H_n(B, \mathbb{L})$▫, where ▫$M^n, \, X^n$▫ are topological manifolds of dimension ▫$n \ge 5$▫. Our proof uses essentially the geometrically defined ▫$\mathbb{L}$▫-spectrum as described by Nicas (going back to Quinn) and some well-known homotopy theory. We also outline the construction of the algebraically defined obstruction, and we explicitly describe the assembly map ▫$H_n(B,L) \to L_n(\pi_1(B))$▫ in terms of forms in the case ▫$n \equiv 0(4)$▫. Finally, we explicitly determine the canonical map ▫$H_n(B,L) \to H_n(B, \, L_0)$▫.
    Vir: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 16, iss. 3, June 2019, art. 79 (22 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 18630745

    Povezava(-e):

    https://doi.org/10.1007/s00009-019-1354-6
    Repozitorij Univerze v Ljubljani – RUL
    DOI

vir: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 16, iss. 3, June 2019, art. 79 (22 str.))
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