Friedman, Greg \(K\)-Witt bordism in characteristic 2. (English) Zbl 1266.55002 Arch. Math. 100, No. 4, 381-387 (2013). A Witt space is a \(\mathbb{Z}\)-oriented piecewise linear stratified pseudomanifold such that the lower middle perversity, rational, middle dimensional intersection homology of links of odd-codimensional strata vanishes. The corresponding bordism theory was computed by Paul Siegel in terms of the Witt groups of the rational numbers. More generally, imposing this vanishing condition on intersection homology with coefficients in any field \(k\), one obtains the class of \(k\)-Witt spaces, considered earlier by G. Friedman [Commun. Pure Appl. Math. 62, No. 9, 1265–1292 (2009); corrigendum ibid. 65, No. 11, 1639–1640 (2012; Zbl 1175.55005)]. The case of characteristic \(2\) is special because in characteristic \(2\) the notions of skew-symmetric and symmetric forms coincide. This case is treated carefully in the paper under review. Whether or not the map from \(\mathbb{Z}_2\)-Witt bordism in degrees \(4k+2\) to the Witt group of \(\mathbb{Z}_2\), given by the intersection form, is surjective remains open. A complete computation for unoriented bordism is obtained. The latter result has also been established by M. Goresky. Reviewer: Markus Banagl (Heidelberg) Cited in 1 Document MathOverflow Questions: Are there oriented \(4k+2\) manifolds such that \(im(H_{2k+1}(M; Z/2)\to H_{2k+1}(M, \partial M; Z/2))\) has odd dimension? MSC: 55N33 Intersection homology and cohomology in algebraic topology Keywords:intersection homology; Witt bordism; Witt space Citations:Zbl 1175.55005 Software:MathOverflow PDFBibTeX XMLCite \textit{G. Friedman}, Arch. Math. 100, No. 4, 381--387 (2013; Zbl 1266.55002) Full Text: DOI arXiv References: [1] Friedman G.: Intersection homology with field coefficients: K-Witt spaces and K-Witt bordism, Comm. Pure Appl. Math. 62, 1265-1292 (2009) · Zbl 1175.55005 [2] Goresky M., MacPherson R.: Intersection homology theory. Topology 19, 135-162 (1980) · Zbl 0448.55004 [3] Goresky M., Siegel P.: Linking pairings on singular spaces, Comment. Math. Helvetici 58, 96-110 (1983) · Zbl 0529.55008 [4] Mark Goresky R.: Intersection homology operations, Comment. Math. Helv. 59, 485-505 (1984) · Zbl 0549.55014 [5] A. Hatcher, Algebraic topology, Cambridge University Press, Cambridge, 2002. · Zbl 1044.55001 [6] King H. C.: Topological invariance of intersection homology without sheaves . Topology Appl. 20, 149-160 (1985) · Zbl 0568.55003 [7] J. Milnor and D. Husemoller, Symmetric bilinear forms, Springer Verlag, New York, 1973. · Zbl 0292.10016 [8] J. R. Munkres, Elements of algebraic topology, Addison-Wesley, Reading, MA, 1984. · Zbl 0673.55001 [9] O. Martin, see http://mathoverflow.net/questions/53419/. [10] Pardon W. L.: Intersection homology Poincaré spaces and the characteristic variety theorem, Comment. Math. Helvetici 65, 198-233 (1990) · Zbl 0707.57017 [11] P.H. Siegel, Witt spaces: a geometric cycle theory for KO-homology at odd primes, American J. Math. 110 (1934), 571-92. · Zbl 0529.55008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.