Fetching the paper…
Reading the bibliography…
We show how the Atiyah-Singer family index theorem for both, usual and self-adjoint elliptic operators fits naturally into the framework of the Madsen-Tillmann-Weiss spectra.
M. A. Kervaire: Relative characteristic classes . Amer. J. Math. 79 (1957), 517-558
1957
Earlier work this paper cites.
J. F. Adams: On Chern characters and the structure of the unitary groups . Proceed. of the Cambridge Philosophical Society 57 (1961), 189-199
1961
Earlier work this paper cites.
F. Hirzebruch: Neue topologische Methoden in der algebraischen Geometrie . Springer-Verlag, (1962)
1962
Earlier work this paper cites.
B. L. Reinhart: Cobordism and the Euler number . Topology 2 (1963) 173-177
1963
Earlier work this paper cites.
D. W. Anderson: The real K K -Theory of classifying spaces . Proc. National Acad. Sci. U.S.A. 51 (1964), 634-636
1964
Earlier work this paper cites.
N. H. Kuiper: The homotopy type of the unitary group of Hilbert space . Topology 3 (1965), 19-30
1965
Earlier work this paper cites.
J. W. Milnor; J. C. Moore: On the structure of Hopf algebras . Ann. of Math. 81 (1965), 211-264
1965
Earlier work this paper cites.
M. F. Atiyah; I. M. Singer: The index of elliptic operators III . Ann. of Math. 87 (1968), 546-604
1968
Earlier work this paper cites.
M. F. Atiyah: The signature of fibre bundles. Global Analysis (Papers in Honor of K. Kodaira), pp. 73-84. Univ. Tokyo Press, Tokyo (1969)
1969
Earlier work this paper cites.
M. F. Atiyah; G. Segal: Equivariant K-Theory and completion . J. Differential Geometry 3 (1969)
1969
Earlier work this paper cites.
M. F. Atiyah; I. M. Singer: Index theory for skew-adjoint Fredholm operators . Publ. Math. IHES 37 (1969), 5-26
1969
Earlier work this paper cites.
M. F. Atiyah; I. M. Singer: The index of elliptic operators IV . Ann. of Math. 93 (1971), 119-138
1971
Earlier work this paper cites.
M. F. Atiyah; I. M. Singer: The index of elliptic operators V . Ann. of Math. 93 (1971), 139-149
1971
Earlier work this paper cites.
W. Meyer: Die Signatur von Faserbündeln und lokalen Koeffizientensystemen . Bonner Mathematische Schriften 53 (1972)
1972
Earlier work this paper cites.
J. F. Adams: Chern characters revisited . Illinois Journal of Mathematics 17 (1973), 333-336
1973
Cited alongside, same era.
J. W. Milnor; J. Stasheff: Characteristic classes . Annals of Mathematics Studies, No. 76. Princeton University Press, Princeton, N. J. (1974)
1974
Cited alongside, same era.
J. C. Becker; D. H. Gottlieb: The transfer map and fiber bundles . Topology 14 (1975), 1-12
1975
Cited alongside, same era.
M. F. Atiyah; V. K. Patodi; I. M. Singer: Spectral asymmetry and Riemannian geometry III . Math. Proc. Cambridge Philos. Soc 79 (1976), 71-99
1976
Cited alongside, same era.
D. Mumford: Towards an enumerative geometry of the moduli space of curves . Arithmetic and geometry, Vol. II, 271-328, Progr. Math., 36, Birkhüser Boston, Boston, MA, 1983
1983
Cited alongside, same era.
M. F. Atiyah; G. Segal: Twisted K K -theory . Ukr. Mat. Visn. 1 (2004), 287-330
2004
Later among the works it cites.
C. Douglas: On the fibrewise Poincaré-Hopf Theorem . Recent developments in algebraic topology, 101-111, Contemp. Math. 407, A.M.S., Providence, RI, 2006
2006
Later among the works it cites.
S. Galatius: Mod 2 homology of the stable spin mapping class group . Math. Ann. 334 (2006), 439-455
2006
Later among the works it cites.
S. Galatius; I. Madsen, U. Tillmann: Divisibility of the stable Miller-Morita-Mumford classes , J. of the A.M.S., 19 (2006), 759-779
2006
Later among the works it cites.
2007
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
E. Y. Miller: The homology of the mapping class group . J. Differential Geom. 24 (1986), 1-14
1986
Cited alongside, same era.
S. Morita: Characteristic classes of surface bundles . Invent. Math. 90 (1987), 551-577
1987
Cited alongside, same era.
H. B. Lawson; M. Michelsohn: Spin geometry . Princeton University Press, (1989)
1989
Cited alongside, same era.
W. Lück; A. Ranicki: Surgery obstructions in fiber bundles . J. Pure Appl. Algebra 81 (1992), 139-189
1992
Cited alongside, same era.
J. F. Adams: Stable homotopy and generalised homology . Reprint of the 1974 original. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, (1995)
1995
Cited alongside, same era.
U. Tillmann: On the homotopy of the stable mapping class group . Invent. Math. 130 (1997), 257-275
1997
Cited alongside, same era.
Y. B. Rudyak: On Thom spectra, orientability and cobordism . Springer-Verlag, 1998
1998
Cited alongside, same era.
2007
Later among the works it cites.
I. Madsen; M. Weiss: The stable moduli space of Riemann surfaces: Mumford’s conjecture . Ann. of Math. 165 (2007), 843-941
2007
Later among the works it cites.
G. Pappas: Integral Riemann-Roch theorem . Invent. Math. 170 (2007), 455-481
2007
Later among the works it cites.
M. Karoubi: K-Theory. An Introduction. Reprint of the 1978 edition, Springer-Verlag 2008
2008
Later among the works it cites.
U. Bunke: Index Theory, Eta Forms, and Deligne Cohomology . Memoirs of the American Mathematical Society 198 (2009)
2009
Closest in time.
2009
Closest in time.
S. Galatius; I. Madsen; U. Tillmann; M. Weiss: The homotopy type of the cobordism category . Acta Math. 202, (2009), 195-239
2009
Closest in time.