Additivity and non-additivity for perverse signatures
By Greg Friedman, Eugénie Hunsicker. 2009
83 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f7c7cda035d05b1f038f2679c96f53c4520b3675
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Singular Intersection Homology (2020, background): “It is also not true, in general, that the perverse signatures satisfy Novikov additivity, but they do have a Wall non-additivity formula, which can be found in [96].”