Periodic cyclic cohomology Chern character for pseudomanifolds with one singular stratum

Chan, Shing-wai

doi:10.1090/S0002-9939-98-04377-9

Periodic cyclic cohomology Chern character for pseudomanifolds with one singular stratum
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by Shing-wai Chan

Proc. Amer. Math. Soc. 126 (1998), 669-675

DOI: https://doi.org/10.1090/S0002-9939-98-04377-9

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Abstract:

We compute the periodic cyclic cohomology Chern character of an admissible pseudomanifold $X^{\dagger }$ with one singular stratum. As a corollary, we obtain the index theorem and spectral flow for signature operators.

References

Jonathan Block and Jeffrey Fox, Asymptotic pseudodifferential operators and index theory, Geometric and topological invariants of elliptic operators (Brunswick, ME, 1988) Contemp. Math., vol. 105, Amer. Math. Soc., Providence, RI, 1990, pp. 1–32. MR 1047274, DOI 10.1090/conm/105/1047274
S. W. Chan, $\mathcal {L}$-classes on Pseudomanifolds with One Singular Stratum, Proc. Amer. Math. Soc. 125 (1997), 1955-1968.
Alain Connes, Noncommutative geometry, Academic Press, Inc., San Diego, CA, 1994. MR 1303779
Alain Connes and Henri Moscovici, Transgression and the Chern character of finite-dimensional $K$-cycles, Comm. Math. Phys. 155 (1993), no. 1, 103–122. MR 1228528, DOI 10.1007/BF02100052
Ezra Getzler, Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem, Comm. Math. Phys. 92 (1983), no. 2, 163–178. MR 728863, DOI 10.1007/BF01210843
Ezra Getzler, The odd Chern character in cyclic homology and spectral flow, Topology 32 (1993), no. 3, 489–507. MR 1231957, DOI 10.1016/0040-9383(93)90002-D
H. Moscovici and F.-B. Wu, Pontryagin forms for manifolds with framed singular strata, Geom. Funct. Anal. 5 (1995), no. 4, 702–728. MR 1345019, DOI 10.1007/BF01902058