Geometry & Topology Volume 26, issue 4 (2022)

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

Power operations in the Stolz–Teichner program

Tobias Barthel, Daniel Berwick-Evans and Nathaniel Stapleton

Geometry & Topology 26 (2022) 1773–1848

DOI: 10.2140/gt.2022.26.1773

Bibliography

1	M Ando, Isogenies of formal group laws and power operations in the cohomology theories E_n, Duke Math. J. 79 (1995) 423 MR1344767
2	M Ando, Power operations in elliptic cohomology and representations of loop groups, Trans. Amer. Math. Soc. 352 (2000) 5619 MR1637129
3	M F Atiyah, Power operations in K–theory, Q. J. Math. 17 (1966) 165 MR202130
4	M Atiyah, Topological quantum field theories, Inst. Hautes Études Sci. Publ. Math. 68 (1988) 175 MR1001453
5	M Atiyah, G Segal, On equivariant Euler characteristics, J. Geom. Phys. 6 (1989) 671 MR1076708
6	A Baker, Hecke operators as operations in elliptic cohomology, J. Pure Appl. Algebra 63 (1990) 1 MR1037690
7	A Baker, C Thomas, Classifying spaces, Virasoro equivariant bundles, elliptic cohomology and moonshine, preprint (1999)
8	T Barthel, N Stapleton, The character of the total power operation, Geom. Topol. 21 (2017) 385 MR3608717
9	M Batchelor, The structure of supermanifolds, Trans. Amer. Math. Soc. 253 (1979) 329 MR536951
10	K Behrend, P Xu, Differentiable stacks and gerbes, J. Symplectic Geom. 9 (2011) 285 MR2817778
11	D Berwick-Evans, Equivariant elliptic cohomology, gauged sigma models, and discrete torsion, Trans. Amer. Math. Soc. 375 (2021) 369 MR4358671
12	D Berwick-Evans, Supersymmetric field theories and the elliptic index theorem with complex coefficients, Geom. Topol. 25 (2021) 2287 MR4310891
13	D Berwick-Evans, A Tripathy, A model for complex analytic equivariant elliptic cohomology from quantum field theory, preprint (2018) arXiv:1805.04146
14	D Berwick-Evans, A Tripathy, A de Rham model for complex analytic equivariant elliptic cohomology, Adv. Math. 380 (2021) MR4205106
15	D Blottière, Differentiable stacks and Lie groupoids, preprint (2007)
16	L Borisov, A Libgober, Elliptic genera of singular varieties, Duke Math. J. 116 (2003) 319 MR1953295
17	R R Bruner, J P May, J E McClure, M Steinberger, H_∞ ring spectra and their applications, 1176, Springer (1986) MR836132
18	P M Cheung, Supersymmetric field theories and generalized cohomology, PhD thesis, Stanford University (2006) MR2709632
19	P Deligne, J W Morgan, Notes on supersymmetry (following Joseph Bernstein), from: "Quantum fields and strings: a course for mathematicians, I" (editors P Deligne, P Etingof, D S Freed, L C Jeffrey, D Kazhdan, J W Morgan, D R Morrison, E Witten), Amer. Math. Soc. (1999) 41 MR1701597
20	J A Devoto, Equivariant elliptic homology and finite groups, Michigan Math. J. 43 (1996) 3 MR1381597
21	R Dijkgraaf, G Moore, E Verlinde, H Verlinde, Elliptic genera of symmetric products and second quantized strings, Comm. Math. Phys. 185 (1997) 197 MR1463039
22	F Dumitrescu, Superconnections and parallel transport, PhD thesis, University of Notre Dame (2006) MR2711311
23	N Ganter, Orbifold genera, product formulas and power operations, Adv. Math. 205 (2006) 84 MR2254309
24	N Ganter, Stringy power operations in Tate K–theory, preprint (2007) arXiv:math/0701565
25	N Ganter, Hecke operators in equivariant elliptic cohomology and generalized Moonshine, from: "Groups and symmetries" (editors J Harnad, P Winternitz), CRM Proc. Lecture Notes 47, Amer. Math. Soc. (2009) 173 MR2500561
26	N Ganter, Global Mackey functors with operations and n–special lambda rings, preprint (2013) arXiv:1301.4616
27	N Ganter, Power operations in orbifold Tate K–theory, Homology Homotopy Appl. 15 (2013) 313 MR3079210
28	D Gepner, L Meier, On equivariant topological modular forms, preprint (2020) arXiv:2004.10254
29	P G Goerss, M J Hopkins, Moduli spaces of commutative ring spectra, from: "Structured ring spectra" (editors A Baker, B Richter), Lond. Math. Soc. Lect. Note Ser. 315, Cambridge Univ. Press (2004) 151 MR2125040
30	D Grady, D Pavlov, Extended field theories are local and have classifying spaces, preprint (2020) arXiv:2011.01208
31	F Han, Supersymmetric QFTs, super loop spaces and Bismut–Chern character, PhD thesis, University of California, Berkeley (2008) MR2712304
32	H Hohnhold, M Kreck, S Stolz, P Teichner, Differential forms and 0–dimensional supersymmetric field theories, Quantum Topol. 2 (2011) 1 MR2763085
33	H Hohnhold, S Stolz, P Teichner, From minimal geodesics to supersymmetric field theories, from: "A celebration of the mathematical legacy of Raoul Bott" (editor P R Kotiuga), CRM Proc. Lect. Notes 50, Amer. Math. Soc. (2010) 207 MR2648897
34	M J Hopkins, N J Kuhn, D C Ravenel, Generalized group characters and complex oriented cohomology theories, J. Amer. Math. Soc. 13 (2000) 553 MR1758754
35	Z Huan, Quasi-elliptic cohomology and its power operations, J. Homotopy Relat. Struct. 13 (2018) 715 MR3870771
36	P S Landweber, D C Ravenel, R E Stong, Periodic cohomology theories defined by elliptic curves, from: "The Čech centennial" (editors M Cenkl, H Miller), Contemp. Math. 181, Amer. Math. Soc. (1995) 317 MR1320998
37	J Lurie, Elliptic cohomology, III: Tempered cohomology, preprint (2019)
38	J Morava, Moonshine elements in elliptic cohomology, from: "Groups and symmetries" (editors J Harnad, P Winternitz), CRM Proc. Lect. Notes 47, Amer. Math. Soc. (2009) 247 MR2500565
39	E Peterson, Formal geometry and bordism operations, 177, Cambridge Univ. Press (2019) MR3890071
40	C Rezk, Isogenies, power operations, and homotopy theory, from: "Proceedings of the International Congress of Mathematicians, II" (editors S Y Jang, Y R Kim, D W Lee, I Ye), Kyung Moon Sa (2014) 1125 MR3728655
41	C J Schommer-Pries, Central extensions of smooth 2–groups and a finite-dimensional string 2–group, Geom. Topol. 15 (2011) 609 MR2800361
42	C Schommer-Pries, N Stapleton, Singular cohomology from supersymmetric field theories, Adv. Math. 390 (2021) MR4298593
43	S Schwede, Global homotopy theory, 34, Cambridge Univ. Press (2018) MR3838307
44	G Segal, The definition of conformal field theory, from: "Topology, geometry and quantum field theory" (editor U Tillmann), Lond. Math. Soc. Lect. Note Ser. 308, Cambridge Univ. Press (2004) 421 MR2079383
45	A Stoffel, Dimensional reduction and the equivariant Chern character, Algebr. Geom. Topol. 19 (2019) 109 MR3910579
46	A Stoffel, Supersymmetric field theories from twisted vector bundles, Comm. Math. Phys. 367 (2019) 417 MR3936122
47	S Stolz, P Teichner, What is an elliptic object?, from: "Topology, geometry and quantum field theory" (editor U Tillmann), Lond. Math. Soc. Lect. Note Ser. 308, Cambridge Univ. Press (2004) 247 MR2079378
48	S Stolz, P Teichner, Supersymmetric field theories and generalized cohomology, from: "Mathematical foundations of quantum field theory and perturbative string theory" (editors H Sati, U Schreiber), Proc. Sympos. Pure Math. 83, Amer. Math. Soc. (2011) 279 MR2742432
49	N P Strickland, Morava E–theory of symmetric groups, Topology 37 (1998) 757 MR1607736
50	H Tamanoi, Generalized orbifold Euler characteristic of symmetric products and equivariant Morava K–theory, Algebr. Geom. Topol. 1 (2001) 115 MR1805937
51	H Tamanoi, Infinite product decomposition of orbifold mapping spaces, Algebr. Geom. Topol. 9 (2009) 569 MR2491586
52	C B Thomas, Elliptic cohomology, Kluwer (1999) MR1742240