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Academic literature on the topic 'Callias-type operators'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Callias-type operators"

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Braverman, Maxim, and Simone Cecchini. "Callias-Type Operators in von Neumann Algebras." Journal of Geometric Analysis 28, no. 1 (April 18, 2017): 546–86. http://dx.doi.org/10.1007/s12220-017-9832-1.

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Anghel, N. "On the index of Callias-type operators." Geometric and Functional Analysis 3, no. 5 (September 1993): 431–38. http://dx.doi.org/10.1007/bf01896237.

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Kottke, Chris. "An index theorem of Callias type for pseudodifferential operators." Journal of K-theory 8, no. 3 (January 19, 2011): 387–417. http://dx.doi.org/10.1017/is010011014jkt132.

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AbstractWe prove an index theorem for families of pseudodifferential operators generalizing those studied by C. Callias, N. Anghel and others. Specifically, we consider operators on a manifold with boundary equipped with an asymptotically conic (scattering) metric, which have the form D + iΦ, where D is elliptic pseudodifferential with Hermitian symbols, and Φ is a Hermitian bundle endomorphism which is invertible at the boundary and commutes with the symbol of D there. The index of such operators is completely determined by the symbolic data over the boundary. We use the scattering calculus of R. Melrose in order to prove our results using methods of topological K-theory, and we devote special attention to the case in which D is a family of Dirac operators, in which case our theorem specializes to give family versions of the previously known index formulas.
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Cecchini, Simone. "Callias-type operators in C∗-algebras and positive scalar curvature on noncompact manifolds." Journal of Topology and Analysis 12, no. 04 (November 16, 2018): 897–939. http://dx.doi.org/10.1142/s1793525319500687.

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A Dirac-type operator on a complete Riemannian manifold is of Callias-type if its square is a Schrödinger-type operator with a potential uniformly positive outside of a compact set. We develop the theory of Callias-type operators twisted with Hilbert [Formula: see text]-module bundles and prove an index theorem for such operators. As an application, we derive an obstruction to the existence of complete Riemannian metrics of positive scalar curvature on noncompact spin manifolds in terms of closed submanifolds of codimension one. In particular, when [Formula: see text] is a closed spin manifold, we show that if the cylinder [Formula: see text] carries a complete metric of positive scalar curvature, then the (complex) Rosenberg index on [Formula: see text] must vanish.
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Braverman, Maxim, and Pengshuai Shi. "Cobordism invariance of the index of Callias-type operators." Communications in Partial Differential Equations 41, no. 8 (April 27, 2016): 1183–203. http://dx.doi.org/10.1080/03605302.2016.1183214.

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Bunke, Ulrich. "A K-theoretic relative index theorem and Callias-type Dirac operators." Mathematische Annalen 303, no. 1 (September 1995): 241–79. http://dx.doi.org/10.1007/bf01460989.

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Shi, Pengshuai. "The index of Callias-type operators with Atiyah–Patodi–Singer boundary conditions." Annals of Global Analysis and Geometry 52, no. 4 (September 6, 2017): 465–82. http://dx.doi.org/10.1007/s10455-017-9575-z.

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Braverman, Maxim, and Pengshuai Shi. "The Index of a Local Boundary Value Problem for Strongly Callias-Type Operators." Arnold Mathematical Journal 5, no. 1 (March 2019): 79–96. http://dx.doi.org/10.1007/s40598-019-00110-1.

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Guo, Hao. "Index of Equivariant Callias-Type Operators and Invariant Metrics of Positive Scalar Curvature." Journal of Geometric Analysis, July 30, 2019. http://dx.doi.org/10.1007/s12220-019-00249-5.

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Dissertations / Theses on the topic "Callias-type operators"

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Guo, Hao. "Positive scalar curvature and Callias-type index theorems for proper actions." Thesis, 2018. http://hdl.handle.net/2440/118136.

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This thesis by publication is a study of the equivariant index theory of Dirac operators and Callias-type operators in two distinct settings, namely on cocompact and non-cocompact manifolds with a Lie group action. The first two chapters are a short resumé of Dirac operators and index theory and form a common introduction to the papers in the appendices. Appendix A is joint work with my supervisors, Elder Professor Mathai Varghese and Dr. Hang Wang. For G an almost-connected Lie group acting properly and cocompactly on a manifold M, we study G-index theory of G- invariant Dirac operators. By establishing Poincaré duality for equivariant K-theory and K-homology, we are able to extend the scope of our results to include all elements of equivariant analytic K-homology, which we also show is isomorphic to equivariant geometric K-homology. Our results are applied to prove: a rigidity result for almost-complex manifolds, generalising a vanishing theorem of Hattori; an analogue of Petrie's conjecture; and Lichnerowicz-type obstructions to G-invariant Riemannian metrics on M. Appendix B studies the much more general situation when the quotient M=G is non-compact and G is an arbitrary Lie group. I define G-Callias- type operators and show that they are C*(G)-Fredholm by adapting analysis of Kasparov to new Hilbert C*(G)-module analogues of Sobolev spaces. Questions of adjointability, regularity and essential self-adjointness are addressed in detail. The estimates on G-Callias-type operators are based on the work of Bunke [8] in the non-equivariant context. We construct explicit admissible endomorphisms for G-Callias-type operators from the K-theory of the Higson G-corona of M, a highly non-trivial group. The index theory developed here is applied to prove a general obstruction theorem for G- invariant metrics of positive scalar curvature in the non-cocompact setting.
Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2018
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Book chapters on the topic "Callias-type operators"

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Gesztesy, Fritz, and Marcus Waurick. "Dirac-Type Operators." In The Callias Index Formula Revisited, 55–63. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29977-8_6.

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