Corpus ID: 235421671

Explicit construction of Atiyah-Singer indices for maximally hypoelliptic operators on contact manifolds

@inproceedings{Tian2021ExplicitCO,
  title={Explicit construction of Atiyah-Singer indices for maximally hypoelliptic operators on contact manifolds},
  author={Mi Tian},
  year={2021}
}
The Atiyah-Singer index theorem gives a topological formula for the index of an elliptic differential operator. Enlightening from Alain Connes’ tangent groupoid proof of the index theoremand van Erp’s research for theHeisenberg index theory on contact manifolds, we give an explicit construction of a series of maps, whose induced map in K-theory is the Heisenberg Atiyah-Singer index map on contact manifolds. Our methods derive from Higson’s construction for symbol class inK-theory. 

References

SHOWING 1-10 OF 10 REFERENCES
Index of Elliptic Operators
Ellipticity condition, proper ellipticity and Lopatinskii condition imply the Fredholm property of elliptic problems in bounded domains. In addition, invertibility of limiting problems determines theExpand
TheAtiyah-Singer index formula for subelliptic operators on contactmanifolds
  • Part I. Annals of Mathematics,
  • 2010
The Atiyah-Singer index formula for subelliptic operators on contact manifolds. Part I
The Atiyah-Singer index theorem gives a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from theExpand
On the K-Theory Proof of the Index Theorem
This paper is an exposition of the K-theory proof of the Atiyah-Singer Index Theorem. I have tried to separate, as much as possible, the analytic parts of the proof from the topological calculations.Expand
Higher Index Theory
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions isExpand
Higher index theory, volume 189
  • 2020
Quantization on Nilpotent Lie Groups
Preface.- Introduction.- Notation and conventions.- 1 Preliminaries on Lie groups.- 2 Quantization on compact Lie groups.- 3 Homogeneous Lie groups.- 4 Rockland operators and Sobolev spaces.- 5Expand
An index theorem for gauge-invariant families: The case of solvable groups
AbstractWe define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $$\mathcal{G} \to B$$ of Lie groups (these families are calledExpand
Noncommutative Geometry
Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. InExpand
The Index of Elliptic Operators: IV