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A Result in Surgery Theory

Published online by Cambridge University Press:  20 November 2018

Alberto Cavicchioli  and
Fulvia Spaggiari
Alberto Cavicchioli
Affiliation:
Dipartimento di Matematica, Università di Modena e di Reggio Emilia, 41100 Modena, Italy. e-mail: [email protected], e-mail: [email protected]
Fulvia Spaggiari
Affiliation:
Dipartimento di Matematica, Università di Modena e di Reggio Emilia, 41100 Modena, Italy. e-mail: [email protected], e-mail: [email protected]
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Abstract

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We study the topological 4-dimensional surgery problem for a closed connected orientable topological 4-manifold $X$ with vanishing second homotopy and ${{\pi }_{1}}\left( X \right)\,\cong \,A\,*\,F\left( r \right)$ , where $A$ has one end and $F\left( r \right)$ is the free group of rank $r\,\ge \,1$. Our result is related to a theorem of Krushkal and Lee, and depends on the validity of the Novikov conjecture for such fundamental groups.

Keywords

57N6557R6757Q10four-manifoldshomotopy typeobstruction theoryhomology with local coefficientssurgerynormal invariantassembly map
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 4 , 01 December 2008 , pp. 508 - 518
Copyright
Copyright © Canadian Mathematical Society 2008

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