English

Cut and paste invariants of manifolds via algebraic K-theory

Algebraic Topology 2021-12-07 v2 Geometric Topology K-Theory and Homology

Abstract

Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic KK-theory, and applying these tools to studying the Grothendieck ring of varieties. In this paper we give a new application of their framework: we construct a KK-space that recovers the classical SK\mathrm{SK} ("schneiden und kleben," German for "cut and paste") groups for manifolds on π0\pi_0, and we construct a derived version of the Euler characteristic.

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Cite

@article{arxiv.2001.00176,
  title  = {Cut and paste invariants of manifolds via algebraic K-theory},
  author = {Renee S. Hoekzema and Mona Merling and Laura Murray and Carmen Rovi and Julia Semikina},
  journal= {arXiv preprint arXiv:2001.00176},
  year   = {2021}
}

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