Algebraic & Geometric Topology Volume 25, issue 6 (2025)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Other MSP journals

A $K$-theory spectrum for cobordism cut and paste groups

Renee S Hoekzema, Carmen Rovi and Julia Semikina

Algebraic & Geometric Topology 25 (2025) 3287–3314

DOI: 10.2140/agt.2025.25.3287

Bibliography

1	M F Atiyah, I M Singer, The index of elliptic operators, III, Ann. of Math. 87 (1968) 546 MR236952
2	A K Bousfield, E M Friedlander, Homotopy theory of Γ-spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory" (editors M G Barratt, M E Mahowald), Lecture Notes in Math. 658, Springer (1978) 80 MR513569
3	J Campbell, J Kuijper, M Merling, I Zakharevich, Algebraic K-theory for squares categories, preprint (2023) arXiv:2310.02852
4	J Ebert, O Randal-Williams, Semisimplicial spaces, Algebr. Geom. Topol. 19 (2019) 2099 MR3995026
5	S Galatius, U Tillmann, I Madsen, M Weiss, The homotopy type of the cobordism category, Acta Math. 202 (2009) 195 MR2506750
6	J Genauer, Cobordism categories of manifolds with corners, Trans. Amer. Math. Soc. 364 (2012) 519 MR2833590
7	R S Hoekzema, M Merling, L Murray, C Rovi, J Semikina, Cut and paste invariants of manifolds via algebraic K-theory, Topology Appl. 316 (2022) 108105 MR4438950
8	U Karras, M Kreck, W D Neumann, E Ossa, Cutting and pasting of manifolds ; SK-groups, 1, Publish or Perish (1973) MR362360
9	R C Kirby, The topology of 4-manifolds, 1374, Springer (1989) MR1001966
10	H K Nguyen, On the infinite loop space structure of the cobordism category, Algebr. Geom. Topol. 17 (2017) 1021 MR3623680
11	G Raptis, W Steimle, Parametrized cobordism categories and the Dwyer–Weiss–Williams index theorem, J. Topol. 10 (2017) 700 MR3665408
12	G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR353298
13	W Steimle, An additivity theorem for cobordism categories, Algebr. Geom. Topol. 21 (2021) 601 MR4250512
14	C T C Wall, Non-additivity of the signature, Invent. Math. 7 (1969) 269 MR246311
15	H E Winkelnkemper, On equators of manifolds and the action of 𝜃ⁿ, PhD thesis, Princeton University (1971)