---
title: "Cut and paste invariants of manifolds via algebraic K-theory" 
---

# Cut and paste invariants of manifolds via algebraic K-theory

## Meta

- CiteKey: "HMM+21"
- Type: journalArticle
- Author: "Hoekzema, Renee S.; Merling, Mona; Murray, Laura; Rovi, Carmen; Semikina, Julia;"  
- Year: 2022 
- DOI: 10.1016/j.topol.2022.108105
- Collections: "Syllabus; Talbot 2022,"
- **Original URL**: <https://www.sciencedirect.com/science/article/pii/S0166864122001079>
- Open local files directly: [Hoekzema et al. - 2022 - Cut and paste invariants of manifolds via algebrai.pdf](file:///home/zack/Downloads/Zotero_Source/Topology%20and%20its%20Applications/2022/Hoekzema%20et%20al.%20-%202022%20-%20Cut%20and%20paste%20invariants%20of%20manifolds%20via%20algebrai.pdf); [ScienceDirect Snapshot](file:///home/zack/Zotero/storage/5VM3CFDZ/S0166864122001079.html)
- **Open in Zotero**: [Zotero](zotero://select/library/items/QLVYQ3JJ)

## 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 π0, and we construct a derived version of the Euler characteristic.

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## Extracted Annotations


Annotations(6/8/2022, 6:58:06 PM)

![[HMM+21_DC84UMJ8.png]] [(Hoekzema et al., 2022, p. 2)](zotero://open-pdf/library/items/FTBJBTZG?page=2&annotation=HWHUSWRF)

![[HMM+21_4C5TQ9YU.png]] [(Hoekzema et al., 2022, p. 2)](zotero://open-pdf/library/items/FTBJBTZG?page=2&annotation=XUCH9GME)

![[HMM+21_5PE4RNGG.png]] [(Hoekzema et al., 2022, p. 2)](zotero://open-pdf/library/items/FTBJBTZG?page=2&annotation=GMQNA83Q)

![[HMM+21_DCWX4IL7.png]] [(Hoekzema et al., 2022, p. 3)](zotero://open-pdf/library/items/FTBJBTZG?page=3&annotation=6X78JUIC)

![[HMM+21_6AJ8EL2E.png]] [(Hoekzema et al., 2022, p. 3)](zotero://open-pdf/library/items/FTBJBTZG?page=3&annotation=FS2LB8DX)

![[HMM+21_QNTITPAS.png]] [(Hoekzema et al., 2022, p. 4)](zotero://open-pdf/library/items/FTBJBTZG?page=4&annotation=6RGFLMVA)

![[HMM+21_3RWKBK7B.png]] [(Hoekzema et al., 2022, p. 5)](zotero://open-pdf/library/items/FTBJBTZG?page=5&annotation=K4D3FJ7V)

![[HMM+21_XJIGE928.png]] [(Hoekzema et al., 2022, p. 6)](zotero://open-pdf/library/items/FTBJBTZG?page=6&annotation=CJNEQIII)

![[HMM+21_S7H8GJUJ.png]] [(Hoekzema et al., 2022, p. 6)](zotero://open-pdf/library/items/FTBJBTZG?page=6&annotation=K6BEGEKF)

![[HMM+21_WPXFW6N9.png]] [(Hoekzema et al., 2022, p. 7)](zotero://open-pdf/library/items/FTBJBTZG?page=7&annotation=H7BMF223)

![[HMM+21_4EZ4NMG3.png]] [(Hoekzema et al., 2022, p. 8)](zotero://open-pdf/library/items/FTBJBTZG?page=8&annotation=96LM4SXV)

![[HMM+21_HKCKFJPC.png]] [(Hoekzema et al., 2022, p. 8)](zotero://open-pdf/library/items/FTBJBTZG?page=8&annotation=U85HERQK)

![[HMM+21_QIA7SKEL.png]] [(Hoekzema et al., 2022, p. 10)](zotero://open-pdf/library/items/FTBJBTZG?page=10&annotation=Z6SNI2BC)

![[HMM+21_QBC66G4D.png]] [(Hoekzema et al., 2022, p. 11)](zotero://open-pdf/library/items/FTBJBTZG?page=11&annotation=E4M89SLF)

![[HMM+21_LS44WDMP.png]] [(Hoekzema et al., 2022, p. 11)](zotero://open-pdf/library/items/FTBJBTZG?page=11&annotation=JGG5DTC3)

![[HMM+21_MPSL99GJ.png]] [(Hoekzema et al., 2022, p. 11)](zotero://open-pdf/library/items/FTBJBTZG?page=11&annotation=DLHNJFLC)

![[HMM+21_66LRB2ZW.png]] [(Hoekzema et al., 2022, p. 12)](zotero://open-pdf/library/items/FTBJBTZG?page=12&annotation=6AILTAX3)

![[HMM+21_N2BJG3VS.png]] [(Hoekzema et al., 2022, p. 12)](zotero://open-pdf/library/items/FTBJBTZG?page=12&annotation=GSFHPTKE)

![[HMM+21_MWKEJAYP.png]] [(Hoekzema et al., 2022, p. 15)](zotero://open-pdf/library/items/FTBJBTZG?page=15&annotation=7ZULRGK4)

![[HMM+21_FCK84MLM.png]] [(Hoekzema et al., 2022, p. 16)](zotero://open-pdf/library/items/FTBJBTZG?page=16&annotation=CQJWS55S)

![[HMM+21_26AGJZ54.png]] [(Hoekzema et al., 2022, p. 19)](zotero://open-pdf/library/items/FTBJBTZG?page=19&annotation=9J8E48SJ)

![[HMM+21_CZJ3R8AF.png]] [(Hoekzema et al., 2022, p. 19)](zotero://open-pdf/library/items/FTBJBTZG?page=19&annotation=ERS9688A)

![[HMM+21_K79KQRBJ.png]] [(Hoekzema et al., 2022, p. 21)](zotero://open-pdf/library/items/FTBJBTZG?page=21&annotation=US6YHEIB)