Volume 18, issue 5 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Other MSP Journals
The factorization theory of Thom spectra and twisted nonabelian Poincaré duality

Inbar Klang

Algebraic & Geometric Topology 18 (2018) 2541–2592
1 M Ando, A J Blumberg, D Gepner, Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map, preprint (2011) arXiv:1112.2203
2 M Ando, A J Blumberg, D Gepner, M J Hopkins, C Rezk, An –categorical approach to R–line bundles, R–module Thom spectra, and twisted R–homology, J. Topol. 7 (2014) 869 MR3252967
3 M Ando, A J Blumberg, D Gepner, M J Hopkins, C Rezk, Units of ring spectra, orientations and Thom spectra via rigid infinite loop space theory, J. Topol. 7 (2014) 1077 MR3286898
4 D Ayala, J Francis, Zero-pointed manifolds, preprint (2014) arXiv:1409.2857
5 D Ayala, J Francis, Factorization homology of topological manifolds, J. Topol. 8 (2015) 1045 MR3431668
6 M Barratt, S Priddy, On the homology of non-connected monoids and their associated groups, Comment. Math. Helv. 47 (1972) 1 MR0314940
7 J Beardsley, Relative Thom spectra via operadic Kan extensions, Algebr. Geom. Topol. 17 (2017) 1151 MR3623685
8 J Beardsley, Topological Hochschild homology of X(n), preprint (2017) arXiv:1708.09486
9 A J Blumberg, Topological Hochschild homology of Thom spectra which are E ring spectra, J. Topol. 3 (2010) 535 MR2684512
10 A J Blumberg, R L Cohen, C Schlichtkrull, Topological Hochschild homology of Thom spectra and the free loop space, Geom. Topol. 14 (2010) 1165 MR2651551
11 I Bobkova, A Lindenstrauss, K Poirier, B Richter, I Zakharevich, On the higher topological Hochschild homology of 𝔽p and commutative 𝔽p–group algebras, from: "Women in topology: collaborations in homotopy theory" (editors M Basterra, K Bauer, K Hess, B Johnson), Contemp. Math. 641, Amer. Math. Soc. (2015) 97 MR3380071
12 F R Cohen, Braid orientations and bundles with flat connections, Invent. Math. 46 (1978) 99 MR493954
13 F R Cohen, J P May, L R Taylor, K(Z,0) and K(Z2,0) as Thom spectra, Illinois J. Math. 25 (1981) 99 MR602900
14 R L Cohen, Stable proofs of stable splittings, Math. Proc. Cambridge Philos. Soc. 88 (1980) 149 MR569640
15 R L Cohen, J D S Jones, A homotopy theoretic realization of string topology, Math. Ann. 324 (2002) 773 MR1942249
16 R L Cohen, J D S Jones, Gauge theory and string topology, Bol. Soc. Mat. Mex. 23 (2017) 233 MR3633134
17 E S Devinatz, M J Hopkins, J H Smith, Nilpotence and stable homotopy theory, I, Ann. of Math. 128 (1988) 207 MR960945
18 B Dundas, A Lindenstrauss, B Richter, Towards an understanding of ramified extensions of structured ring spectra, Math. Proc. Cambridge Philos. Soc. (2018)
19 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, 47, Amer. Math. Soc. (1997) MR1417719
20 J Francis, The tangent complex and Hochschild cohomology of n–rings, Compos. Math. 149 (2013) 430 MR3040746
21 V Franjou, J Lannes, L Schwartz, Autour de la cohomologie de Mac Lane des corps finis, Invent. Math. 115 (1994) 513 MR1262942
22 V Franjou, T Pirashvili, On the Mac Lane cohomology for the ring of integers, Topology 37 (1998) 109 MR1480880
23 D Gepner, M Groth, T Nikolaus, Universality of multiplicative infinite loop space machines, Algebr. Geom. Topol. 15 (2015) 3107 MR3450758
24 G Ginot, T Tradler, M Zeinalian, Higher Hochschild cohomology, Brane topology and centralizers of En–algebra maps, preprint (2012) arXiv:1205.7056
25 G Ginot, T Tradler, M Zeinalian, Higher Hochschild homology, topological chiral homology and factorization algebras, Comm. Math. Phys. 326 (2014) 635 MR3173402
26 K Gruher, P Salvatore, Generalized string topology operations, Proc. Lond. Math. Soc. 96 (2008) 78 MR2392316
27 K Hess, P E Parent, J Scott, CoHochschild homology of chain coalgebras, J. Pure Appl. Algebra 213 (2009) 536 MR2483836
28 G Horel, Operads, modules and topological field theories, preprint (2014) arXiv:1405.5409
29 G Horel, Higher Hochschild cohomology of the Lubin–Tate ring spectrum, Algebr. Geom. Topol. 15 (2015) 3215 MR3450760
30 G Horel, Factorization homology and calculus à la Kontsevich Soibelman, J. Noncommut. Geom. 11 (2017) 703 MR3669116
31 P Hu, Higher string topology on general spaces, Proc. London Math. Soc. 93 (2006) 515 MR2251161
32 P Hu, I Kriz, A A Voronov, On Kontsevich’s Hochschild cohomology conjecture, Compos. Math. 142 (2006) 143 MR2197407
33 B Knudsen, Betti numbers and stability for configuration spaces via factorization homology, Algebr. Geom. Topol. 17 (2017) 3137 MR3704255
34 A Kupers, J Miller, En–cell attachments and a local-to-global principle for homological stability, Math. Ann. 370 (2018) 209 MR3747486
35 L G Lewis Jr., J P May, M Steinberger, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
36 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
37 J Lurie, Higher algebra, book project (2017)
38 M Mahowald, D C Ravenel, P Shick, The Thomified Eilenberg–Moore spectral sequence, from: "Cohomological methods in homotopy theory" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 249 MR1851257
39 E J Malm, String topology and the based loop space, preprint (2011) arXiv:1103.6198
40 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
41 J P May, What precisely are E ring spaces and E ring spectra ?, from: "New topological contexts for Galois theory and algebraic geometry" (editors A Baker, B Richter), Geom. Topol. Monogr. 16, Geom. Topol. Publ. (2009) 215 MR2544391
42 D McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975) 91 MR0358766
43 J Miller, Nonabelian Poincaré duality after stabilizing, Trans. Amer. Math. Soc. 367 (2015) 1969 MR3286505
44 S Priddy, K(Z∕2) as a Thom spectrum, Proc. Amer. Math. Soc. 70 (1978) 207 MR0474271
45 D C Ravenel, Complex cobordism and stable homotopy groups of spheres, 347, Amer. Math. Soc. (2004) MR860042
46 P Salvatore, Configuration spaces with summable labels, from: "Cohomological methods in homotopy theory" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 375 MR1851264
47 P Salvatore, Configuration spaces on the sphere and higher loop spaces, Math. Z. 248 (2004) 527 MR2097373
48 P Salvatore, N Wahl, Framed discs operads and Batalin–Vilkovisky algebras, Q. J. Math. 54 (2003) 213 MR1989873
49 C Schlichtkrull, Units of ring spectra and their traces in algebraic K–theory, Geom. Topol. 8 (2004) 645 MR2057776
50 C Schlichtkrull, Higher topological Hochschild homology of Thom spectra, J. Topol. 4 (2011) 161 MR2783381
51 S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. 80 (2000) 491 MR1734325
52 G Segal, Locality of holomorphic bundles, and locality in quantum field theory, from: "The many facets of geometry" (editors O García-Prada, J P Bourguignon, S Salamon), Oxford Univ. Press (2010) 164 MR2681691
53 T Veen, Detecting periodic elements in higher topological Hochschild homology, Geom. Topol. 22 (2018) 693 MR3748678