2009, 16: 37-43. doi: 10.3934/era.2009.16.37

On the analyticity of the bivariant JLO cocycle

1. 

UMR 7122, Universit Paul Verlaine-Metz, Bt. A, Ile du Saulcy, F-57045 METZ Cedex 1, France

2. 

Mathematical Sciences Institute, Australian National University, Canberra, ACT. 0200, Australia

Received  December 2008 Revised  June 2009 Published  July 2009

The goal of this note is to outline a proof that, for any l $\geq 0$, the JLO bivariant cocycle associated with a family of Dirac type operators along a smooth fibration $M\to B$ over the pair of algebras $(C^\infty (M), C^\infty(B))$, is entire when we endow $C^\infty(M)$ with the $C^{l+1}$ topology and $C^\infty(B)$ with the $C^{l}$ topology. As a corollary, we deduce that this cocycle is analytic when we consider the Fréchet smooth topologies on $C^\infty(M)$ and $C^\infty(B)$.
Citation: Moulay-Tahar Benameur, Alan L. Carey. On the analyticity of the bivariant JLO cocycle. Electronic Research Announcements, 2009, 16: 37-43. doi: 10.3934/era.2009.16.37
[1]

Z. Reichstein and B. Youssin. Parusinski's "Key Lemma" via algebraic geometry. Electronic Research Announcements, 1999, 5: 136-145.

[2]

Daoyin He, Ingo Witt, Huicheng Yin. On the strauss index of semilinear tricomi equation. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4817-4838. doi: 10.3934/cpaa.2020213

[3]

Pengyu Chen. Non-autonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 2725-3737. doi: 10.3934/dcds.2020383

[4]

Peter Benner, Jens Saak, M. Monir Uddin. Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. Numerical Algebra, Control & Optimization, 2016, 6 (1) : 1-20. doi: 10.3934/naco.2016.6.1

[5]

Dayalal Suthar, Sunil Dutt Purohit, Haile Habenom, Jagdev Singh. Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021019

2019 Impact Factor: 0.5

Metrics

  • PDF downloads (32)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]