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On Steenrod 𝕃-homology, generalized manifolds, and surgery

Published online by Cambridge University Press:  20 March 2020

Friedrich Hegenbarth
Affiliation:
Dipartimento di Matematica ‘Federigo Enriques’, Università degli studi di Milano, 20133Milano, Italy (friedrich.hegenbarth@unimi.it)
Dušan Repovš
Affiliation:
Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana & Institute of Mathematics, Physics and Mechanics, 1000Ljubljana, Slovenia (dusan.repovs@guest.arnes.si)

Abstract

The aim of this paper is to show the importance of the Steenrod construction of homology theories for the disassembly process in surgery on a generalized n-manifold Xn, in order to produce an element of generalized homology theory, which is basic for calculations. In particular, we show how to construct an element of the nth Steenrod homology group $H^{st}_{n} (X^{n}, \mathbb {L}^+)$, where 𝕃+ is the connected covering spectrum of the periodic surgery spectrum 𝕃, avoiding the use of the geometric splitting procedure, the use of which is standard in surgery on topological manifolds.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2020

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Footnotes

Dedicated to the memory of Professor Andrew Ranicki (1948–2018)

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