Geometry & Topology Volume 25, issue 7 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Rational Pontryagin classes of Euclidean fiber bundles

Michael S Weiss

Geometry & Topology 25 (2021) 3351–3424

DOI: 10.2140/gt.2021.25.3351

Bibliography

1	J F Adams, Infinite loop spaces, 90, Princeton Univ. Press (1978) MR505692
2	R Andrade, From manifolds to invariants of E_n–algebras, PhD thesis, Massachusetts Institute of Technology (2010) MR2898647
3	S Axelrod, I M Singer, Chern–Simons perturbation theory, II, J. Differential Geom. 39 (1994) 173 MR1258919
4	D Ayala, J Francis, N Rozenblyum, Factorization homology, I : Higher categories, Adv. Math. 333 (2018) 1042 MR3818096
5	A Berglund, J Bergström, Hirzebruch L–polynomials and multiple zeta values, Math. Ann. 372 (2018) 125 MR3856808
6	P Boavida de Brito, M Weiss, Manifold calculus and homotopy sheaves, Homology Homotopy Appl. 15 (2013) 361 MR3138384
7	P Boavida de Brito, M S Weiss, The configuration category of a product, Proc. Amer. Math. Soc. 146 (2018) 4497 MR3834674
8	P Boavida de Brito, M Weiss, Spaces of smooth embeddings and configuration categories, J. Topol. 11 (2018) 65 MR3784227
9	M Brown, Locally flat imbeddings of topological manifolds, Ann. of Math. 75 (1962) 331 MR133812
10	D Burghelea, R Lashof, The homotopy type of the space of diffeomorphisms, I, Trans. Amer. Math. Soc. 196 (1974) 1 MR356103
11	D C Cisinski, I Moerdijk, Dendroidal sets as models for homotopy operads, J. Topol. 4 (2011) 257 MR2805991
12	D C Cisinski, I Moerdijk, Dendroidal Segal spaces and ∞–operads, J. Topol. 6 (2013) 675 MR3100887
13	D C Cisinski, I Moerdijk, Dendroidal sets and simplicial operads, J. Topol. 6 (2013) 705 MR3100888
14	F R Cohen, T J Lada, J P May, The homology of iterated loop spaces, 533, Springer (1976) MR0436146
15	R Connelly, A new proof of Brown’s collaring theorem, Proc. Amer. Math. Soc. 27 (1971) 180 MR267588
16	T tom Dieck, Transformation groups, 8, de Gruyter (1987) MR889050
17	W G Dwyer, D M Kan, Function complexes in homotopical algebra, Topology 19 (1980) 427 MR584566
18	W G Dwyer, D M Kan, An obstruction theory for diagrams of simplicial sets, Nederl. Akad. Wetensch. Indag. Math. 46 (1984) 139 MR749527
19	F T Farrell, W C Hsiang, On the rational homotopy groups of the diffeomorphism groups of discs, spheres and aspherical manifolds, from: "Algebraic and geometric topology, I" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 325 MR520509
20	B Fresse, V Turchin, T Willwacher, The rational homotopy of mapping spaces of E_n operads, preprint (2017) arXiv:1703.06123
21	B Fresse, T Willwacher, Mapping spaces for DG Hopf cooperads and homotopy automorphisms of the rationalization of E_n–operads, preprint (2020) arXiv:2003.02939
22	W Fulton, R MacPherson, A compactification of configuration spaces, Ann. of Math. 139 (1994) 183 MR1259368
23	S Galatius, O Randal-Williams, Stable moduli spaces of high-dimensional manifolds, Acta Math. 212 (2014) 257 MR3207759
24	S Galatius, O Randal-Williams, Homological stability for moduli spaces of high dimensional manifolds, I, J. Amer. Math. Soc. 31 (2018) 215 MR3718454
25	P Goerss, K Schemmerhorn, Model categories and simplicial methods, from: "Interactions between homotopy theory and algebra" (editors L L Avramov, J D Christensen, W G Dwyer, M A Mandell, B E Shipley), Contemp. Math. 436, Amer. Math. Soc. (2007) 3 MR2355769
26	T G Goodwillie, A multiple disjunction lemma for smooth concordance embeddings, 431, Amer. Math. Soc. (1990) MR1015675
27	T G Goodwillie, J R Klein, Multiple disjunction for spaces of Poincaré embeddings, J. Topol. 1 (2008) 761 MR2461855
28	T G Goodwillie, J R Klein, Multiple disjunction for spaces of smooth embeddings, J. Topol. 8 (2015) 651 MR3394312
29	T G Goodwillie, M Weiss, Embeddings from the point of view of immersion theory, II, Geom. Topol. 3 (1999) 103 MR1694808
30	F Göppl, A spectral sequence for spaces of maps between operads, preprint (2018) arXiv:1810.05589
31	P J Hilton, On the homotopy groups of the union of spheres, J. Lond. Math. Soc. 30 (1955) 154 MR68218
32	M W Hirsch, Differential topology, 33, Springer (1976) MR0448362
33	P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
34	F Hirzebruch, Topological methods in algebraic geometry, 131, Springer (1966) MR0202713
35	J Hollender, R M Vogt, Modules of topological spaces, applications to homotopy limits and E_∞ structures, Arch. Math. (Basel) 59 (1992) 115 MR1170635
36	M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
37	K Igusa, The stability theorem for smooth pseudoisotopies, K–Theory 2 (1988) 1 MR972368
38	K Igusa, Higher Franz–Reidemeister torsion, 31, Amer. Math. Soc. (2002) MR1945530
39	R C Kirby, L C Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, 88, Princeton Univ. Press (1977) MR0645390
40	J M Kister, Microbundles are fibre bundles, Ann. of Math. 80 (1964) 190 MR180986
41	M Kontsevich, Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1999) 35 MR1718044
42	A Kosiński, On the inertia group of π–manifolds, Amer. J. Math. 89 (1967) 227 MR214085
43	M Krannich, A homological approach to pseudoisotopy theory, I, (2020) arXiv:2002.04647
44	A Kupers, Some finiteness results for groups of automorphisms of manifolds, Geom. Topol. 23 (2019) 2277 MR4019894
45	P Lambrechts, I Volić, Formality of the little N–disks operad, 1079, Amer. Math. Soc. (2014) MR3220287
46	W Lück, A Ranicki, Surgery obstructions of fibre bundles, J. Pure Appl. Algebra 81 (1992) 139 MR1176019
47	M Mather, Pull-backs in homotopy theory, Canad. J. Math. 28 (1976) 225 MR402694
48	C McTague, Triangle read by rows : numerators of coefficients of the Hirzebruch L–polynomials L_n expressing the signature of a 4n–dimensional manifold in terms of its Pontrjagin numbers (as in Hirzebruch signature theorem), (2014)
49	W Meyer, Die Signatur von lokalen Koeffizientensystemen und Faserbündeln, Bonn. Math. Schr. 1972 (1972) 1 MR305402
50	D A Miller, Popaths and holinks, J. Homotopy Relat. Struct. 4 (2009) 265 MR2559643
51	D A Miller, Strongly stratified homotopy theory, Trans. Amer. Math. Soc. 365 (2013) 4933 MR3066775
52	J Milnor, Microbundles, I, Topology 3 (1964) 53 MR161346
53	J W Milnor, On the construction FK, from: "Algebraic topology : a student’s guide" (editor J F Adams), Lond. Math. Soc. Lect. Note Ser. 4, Cambridge Univ. Press (1972) 118
54	J W Milnor, J D Stasheff, Characteristic classes, 76, Princeton Univ. Press (1974) MR0440554
55	I Moerdijk, I Weiss, Dendroidal sets, Algebr. Geom. Topol. 7 (2007) 1441 MR2366165
56	S Morita, Geometry of characteristic classes, 199, Amer. Math. Soc. (2001) MR1826571
57	C Morlet, Lissage des homéomorphismes, C. R. Acad. Sci. Paris Sér. A-B 269 (1969) 1323 MR268900
58	S P Novikov, Topological invariance of rational classes of Pontrjagin, Dokl. Akad. Nauk SSSR 163 (1965) 298 MR0193644
59	F Quinn, Topological transversality holds in all dimensions, Bull. Amer. Math. Soc. 18 (1988) 145 MR929089
60	O Randal-Williams, An upper bound for the pseudoisotopy stable range, Math. Ann. 368 (2017) 1081 MR3673647
61	O Randal-Williams, A note on the family signature theorem, unpublished note (2019)
62	E Riehl, Categorical homotopy theory, 24, Cambridge Univ. Press (2014) MR3221774
63	V A Rokhlin, A S Schwarz, The combinatorial invariance of Pontrjagin classes, Dokl. Akad. Nauk SSSR 114 (1957) 490 MR0102070
64	C Rovi, The nonmultiplicativity of the signature modulo 8 of a fibre bundle is an Arf–Kervaire invariant, Algebr. Geom. Topol. 18 (2018) 1281 MR3784006
65	S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. Lond. Math. Soc. 80 (2000) 491 MR1734325
66	L C Siebenmann, Classification of sliced families of manifold structures, from: "Foundational essays on topological manifolds, smoothings, and triangulations", Ann. of Math. Studies 88, Princeton Univ. Press (1977) 215 MR0645390
67	D P Sinha, Manifold-theoretic compactifications of configuration spaces, Selecta Math. 10 (2004) 391 MR2099074
68	J D Stasheff, Homotopy associativity of H–spaces, I, Trans. Amer. Math. Soc. 108 (1963) 275 MR0158400
69	J D Stasheff, Homotopy associativity of H–spaces, II, Trans. Amer. Math. Soc. 108 (1963) 293 MR0158400
70	D P Sullivan, Triangulating homotopy equivalences, PhD thesis, Princeton University (1966) MR2615489
71	R Thom, Les classes caractéristiques de Pontrjagin des variétés triangulées, from: "Symposium internacional de topología algebraica", Univ. Nac. Autónoma Mexico (1958) 54 MR0102071
72	S Tillmann, Occupants in simplicial complexes, Algebr. Geom. Topol. 19 (2019) 1265 MR3954282
73	S Tillmann, M S Weiss, Occupants in manifolds, from: "Manifolds and K–theory" (editors G Arone, B Johnson, P Lambrechts, B A Munson, I Volić), Contemp. Math. 682, Amer. Math. Soc. (2017) 237 MR3603901
74	I Volić, Configuration space integrals and Taylor towers for spaces of knots, Topology Appl. 153 (2006) 2893 MR2248391
75	I Volić, Finite type knot invariants and the calculus of functors, Compos. Math. 142 (2006) 222 MR2197410
76	C T C Wall, The action of Γ_2n on (n−1)–connected 2n–manifolds, Proc. Amer. Math. Soc. 13 (1962) 943 MR143223
77	T Watanabe, On Kontsevich’s characteristic classes for higher dimensional sphere bundles, I : The simplest class, Math. Z. 262 (2009) 683 MR2506314
78	T Watanabe, On Kontsevich’s characteristic classes for higher-dimensional sphere bundles, II : Higher classes, J. Topol. 2 (2009) 624 MR2546588
79	M S Weiss, Truncated operads and simplicial spaces, Tunis. J. Math. 1 (2019) 109 MR3907736
80	M S Weiss, Configuration categories and homotopy automorphisms, Glasg. Math. J. 62 (2020) 13 MR4038997