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Published online by Cambridge University Press: 18 September 2020
We introduce Witt and IP spaces, which are the spaces on which middle-dimensional intersection cohomology self-pairings are possible. This leads to signature invariants for such spaces, and we demonstrate their basic properties, including Novikov additivity. Using the signature, we provide in detail the Goresky–MacPherson construction of the characteristic L-classes for Witt spaces, which is modeled upon the classical construction for PL manifolds. We also provide a survey of bordism groups and bordism homology theories based on different types of pseudomanifolds.
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