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Pabiniak, M. and Sabatini, S. (2018). Canonical bases for the equivariant cohomology and K-theory rings of symplectic toric manifolds. J. Symplectic Geom., 16 (4). S. 1117 - 1166. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1540-2347

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Abstract

Let M be a symplectic toric manifold acted on by a torus T. In this work we exhibit an explicit basis for the equivariant K-theory ring K-T(M) which is canonically associated to a generic component of the moment map. We provide a combinatorial algorithm for computing the restrictions of the elements of this basis to the fixed point set; these, in turn, determine the ring structure of K-T(M). The construction is based on the notion of local index at a fixed point, similar to that introduced by Guillemin and Kogan in [GK]. We apply the same techniques to exhibit an explicit basis for the equivariant cohomology ring H-T(M; Z) which is canonically associated to a generic component of the moment map. Moreover we prove that the elements of this basis coincide with some well-known sets of classes: the equivariant Poincare duals to certain smooth flow up submanifolds, and also the canonical classes introduced by Goldin and Tolman in [GT], which exist whenever the moment map is index increasing.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Pabiniak, M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Sabatini, S. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-199616
DOI:	10.4310/JSG.2018.v16.n4.a8
Journal or Publication Title:	J. Symplectic Geom.
Volume:	16
Number:	4
Page Range:	S. 1117 - 1166
Date:	2018
Publisher:	INT PRESS BOSTON, INC
Place of Publication:	SOMERVILLE
ISSN:	1540-2347
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language HAMILTONIAN G-SPACES; CONVEXITY Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/19961