Cut and paste invariants of manifolds via algebraic K-theory

Renee S. Hoekzema; Mona Merling; Laura Murray; Carmen Rovi; Julia Semikina

doi:10.1016/j.topol.2022.108105

Cut and paste invariants of manifolds via algebraic K-theory

Renee S. Hoekzema, Mona Merling, Laura Murray, Carmen Rovi, Julia Semikina

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

Recent work of Inna Zakharevich and Jonathan Campbell has focused on building machinery for studying scissors congruence problems via algebraic K-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 K-theory space that recovers the classical SK (“schneiden und kleben,” German for “cut and paste”) groups for manifolds on , and we construct a derived version of the Euler characteristic.

Original language	English
Article number	108105
Pages (from-to)	1-18
Number of pages	18
Journal	Topology and its Applications
Volume	316
Early online date	15 Apr 2022
DOIs	https://doi.org/10.1016/j.topol.2022.108105
Publication status	Published - 1 Jul 2022

Funding

Finally, we thank the organizers of the Women in Topology III program and the Hausdorff Research Institute for Mathematics for their hospitality during the workshop. The WIT III workshop was supported through grants NSF-DSM 1901795, NSF-HRD 1500481 - AWM ADVANCE grant and the Foundation Compositio Mathematica, and we are very grateful for their support. The first named author was supported by the Max Planck Society. The second named author was supported by grants NSF-DMS 1709461, NSF CAREER DMS 1943925 and NSF FRG DMS-2052988. The third named author was supported by grant NSF-DMS 1547292. The fourth named author is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster), and also wishes to acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) 281869850 (RTG 2229). The fifth named author was supported by the Max Planck Society and Wolfgang Lück's ERC Advanced Grant “KL2MG-interactions” (no. 662400). Finally, we thank the organizers of the Women in Topology III program and the Hausdorff Research Institute for Mathematics for their hospitality during the workshop. The WIT III workshop was supported through grants NSF - DSM 1901795 , NSF - HRD 1500481 - AWM ADVANCE grant and the Foundation Compositio Mathematica, and we are very grateful for their support. The first named author was supported by the Max Planck Society . The second named author was supported by grants NSF - DMS 1709461 , NSF CAREER DMS 1943925 and NSF FRG DMS-2052988 . The third named author was supported by grant NSF - DMS 1547292 . The fourth named author is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster), and also wishes to acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) 281869850 ( RTG 2229 ). The fifth named author was supported by the Max Planck Society and Wolfgang Lück's ERC Advanced Grant “KL2MG-interactions” (no. 662400 ).

Funders	Funder number
Foundation Compositio Mathematica
NSF-DMS	1709461
NSF-DSM	1901795
NSF-HRD	1500481
Wolfgang Lück's ERC
National Science Foundation	FRG DMS-2052988, DMS 1943925, 1547292
Horizon 2020 Framework Programme	662400
Deutsche Forschungsgemeinschaft	281869850, EXC2181/1-390900948, RTG 2229
Max-Planck-Gesellschaft	NSF - DMS 1547292, DMS 1709461
Hausdorff Research Institute for Mathematics

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Cut and paste invariants of manifolds via algebraic K-theory

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