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Title: Additivity and non-additivity for perverse signatures
Authors: Friedman, Greg
Hunsicker, Eugenie
Issue Date: 2013
Publisher: © Walter de Gruyter
Citation: FRIEDMAN, G. and HUNSICKER, E., 2013. Additivity and non-additivity for perverse signatures. Journal für die reine und angewandte Mathematik, 676, pp. 51 - 95.
Abstract: A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifolds with boundary. Wall showed that this property is not true of signatures on manifolds with boundary and that the difference from additivity could be described as a certain Maslov triple index. Perverse signatures are signatures defined for any oriented stratified pseudomanifold, using the intersection homology groups of Goresky and MacPherson. In the case of Witt spaces, the middle perverse signature is the same as the Witt signature. This paper proves a generalization to perverse signatures of Wall's non-additivity theorem for signatures of manifolds with boundary. Under certain topological conditions on the dividing hypersurface, Novikov additivity for perverse signatures may be deduced as a corollary. In particular, Siegel's version of Novikov additivity for Witt signatures is a special case of this corollary.
Description: This article was published in the Journal für die reine und angewandte Mathematik [© Walter de Gruyter]. It is also available at: http://dx.doi.org/10.1515/crelle.2012.005
Sponsor: The authors are partially supported by MSRI.
Version: Published
DOI: 10.1515/crelle.2012.005
URI: https://dspace.lboro.ac.uk/2134/17174
Publisher Link: http://dx.doi.org/10.1515/crelle.2012.005
ISSN: 0075-4102
Appears in Collections:Published Articles (Maths)

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