Geometry & Topology Volume 28, issue 1 (2024)

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

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Embedding calculus and smooth structures

Ben Knudsen and Alexander Kupers

Geometry & Topology 28 (2024) 353–392

DOI: 10.2140/gt.2024.28.353

Bibliography

1	R Andrade, From manifolds to invariants of E_n–algebras, preprint (2012) arXiv:1210.7909
2	P L Antonelli, On stable diffeomorphism of exotic spheres in the metastable range, Canad. J. Math. 23 (1971) 579 MR0283810
3	G Arone, M Szymik, Spaces of knotted circles and exotic smooth structures, Canad. J. Math. 74 (2022) 1 MR4379395
4	J E Bergner, A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007) 2043 MR2276611
5	P Boavida de Brito, M Weiss, Manifold calculus and homotopy sheaves, Homology Homotopy Appl. 15 (2013) 361 MR3138384
6	P Boavida de Brito, M Weiss, Spaces of smooth embeddings and configuration categories, J. Topol. 11 (2018) 65 MR3784227
7	M Brown, A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc. 66 (1960) 74 MR0117695
8	D Burghelea, R Lashof, The homotopy type of the space of diffeomorphisms, I, Trans. Amer. Math. Soc. 196 (1974) 1 MR0356103
9	D Burghelea, R Lashof, The homotopy type of the space of diffeomorphisms, II, Trans. Amer. Math. Soc. 196 (1974) 37 MR0356103
10	D Dugger, D C Isaksen, Topological hypercovers and 𝔸¹–realizations, Math. Z. 246 (2004) 667 MR2045835
11	R D Edwards, R C Kirby, Deformations of spaces of imbeddings, Ann. of Math. 93 (1971) 63 MR0283802
12	M H Freedman, F Quinn, Topology of 4–manifolds, 39, Princeton Univ. Press (1990) MR1201584
13	S Galatius, O Randal-Williams, Moduli spaces of manifolds : a user’s guide, from: "Handbook of homotopy theory" (editor H Miller), CRC (2020) 443 MR4197992
14	T G Goodwillie, J R Klein, Multiple disjunction for spaces of smooth embeddings, J. Topol. 8 (2015) 651 MR3394312
15	T G Goodwillie, J R Klein, M S Weiss, A Haefliger style description of the embedding calculus tower, Topology 42 (2003) 509 MR1953238
16	T G Goodwillie, M Weiss, Embeddings from the point of view of immersion theory, II, Geom. Topol. 3 (1999) 103 MR1694808
17	G Horel, Profinite completion of operads and the Grothendieck–Teichmüller group, Adv. Math. 321 (2017) 326 MR3715714
18	W C Hsiang, J Levine, R H Szczarba, On the normal bundle of a homotopy sphere embedded in Euclidean space, Topology 3 (1965) 173 MR0175138
19	D Husemoller, Fibre bundles, 20, Springer (1994) MR1249482
20	M A Kervaire, Some nonstable homotopy groups of Lie groups, Illinois J. Math. 4 (1960) 161 MR0113237
21	M A Kervaire, On higher dimensional knots, from: "Differential and combinatorial topology (a symposium in honor of Marston Morse)", Princeton Univ. Press (1965) 105 MR178475
22	R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, 88, Princeton Univ. Press (1977) MR0645390
23	J M Kister, Microbundles are fibre bundles, Ann. of Math. 80 (1964) 190 MR0180986
24	M Kontsevich, Feynman diagrams and low-dimensional topology, from: "First European Congress of Mathematics, II" (editors A Joseph, F Mignot, F Murat, B Prum, R Rentschler), Progr. Math. 120, Birkhäuser (1994) 97 MR1341841
25	A Körschgen, Dwyer–Kan equivalences induce equivalences on topologically enriched presheaves, preprint (2017) arXiv:1704.07472
26	M Krannich, A Kupers, Embedding calculus for surfaces, preprint (2021) arXiv:2101.07885
27	M Krannich, A Kupers, The 𝒟isc–structure space, preprint (2022) arXiv:2205.01755
28	A Kupers, Some finiteness results for groups of automorphisms of manifolds, Geom. Topol. 23 (2019) 2277 MR4019894
29	A Kupers, O Randal-Williams, The cohomology of Torelli groups is algebraic, Forum Math. Sigma 8 (2020) MR4190064
30	J Levine, A classification of differentiable knots, Ann. of Math. 82 (1965) 15 MR0180981
31	J Lurie, Higher algebra, preprint (2017)
32	M Mahowald, Some Whitehead products in Sⁿ, Topology 4 (1965) 17 MR0178467
33	M Mahowald, The metastable homotopy of Sⁿ, 72, Amer. Math. Soc. (1967) 81 MR236923
34	M Mahowald, A new infinite family in ₂π_∗^s, Topology 16 (1977) 249 MR0445498
35	M Mahowald, R D Thompson, The EHP sequence and periodic homotopy, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 397 MR1361895
36	W S Massey, On the normal bundle of a sphere imbedded in Euclidean space, Proc. Amer. Math. Soc. 10 (1959) 959 MR0109351
37	J Milnor, Microbundles, I, Topology 3 (1964) 53 MR0161346
38	N Prigge, On tautological classes of fibre bundles and self-embedding calculus, PhD thesis, University of Cambridge (2020)
39	A A Ranicki, On the Hauptvermutung, from: "The Hauptvermutung book", K–Monogr. Math. 1, Kluwer (1996) 3 MR1434101
40	L C Siebenmann, Deformation of homeomorphisms on stratified sets, Comment. Math. Helv. 47 (1972) 123 MR0319207
41	V Turchin, Context-free manifold calculus and the Fulton–MacPherson operad, Algebr. Geom. Topol. 13 (2013) 1243 MR3071127
42	O Viro, Space of smooth 1–knots in a 4–manifold : is its algebraic topology sensitive to smooth structures ?, Arnold Math. J. 1 (2015) 83 MR3331970
43	I Volić, Finite type knot invariants and the calculus of functors, Compos. Math. 142 (2006) 222 MR2197410
44	C T C Wall, Differential topology, 156, Cambridge Univ. Press (2016) MR3558600
45	T Watanabe, Some exotic nontrivial elements of the rational homotopy groups of Diff(S⁴), preprint (2018) arXiv:1812.02448
46	M Weiss, Embeddings from the point of view of immersion theory, I, Geom. Topol. 3 (1999) 67 MR1694812
47	M S Weiss, Rational Pontryagin classes of Euclidean fiber bundles, Geom. Topol. 25 (2021) 3351 MR4372633