Donaldson invariants for non-simply connected manifolds

Marcos Mariño; Gregory Moore

doi:10.1007/s002200050611

Donaldson invariants for non-simply connected manifolds

Marcos Mariño, Gregory Moore

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We study Coulomb branch ("u-plane") integrals for N = 2 supersymmetric SU (2), SO (3) Yang-Mills theory on 4-manifolds X of b₁ (X) > 0, b₂⁺ (X) = 1. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with b₁ (X) > 0, b₂⁺ (X) > 0. Explicit expressions for X = ℂ P¹ × F_g, where F_g is a Riemann surface of genus g are obtained using Kronecker's double series identity. The result might be useful in future studies of quantum cohomology.

Original language	English (US)
Pages (from-to)	249-267
Number of pages	19
Journal	Communications In Mathematical Physics
Volume	203
Issue number	2
DOIs	https://doi.org/10.1007/s002200050611
State	Published - 1999
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s002200050611

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abstract = "We study Coulomb branch ({"}u-plane{"}) integrals for N = 2 supersymmetric SU (2), SO (3) Yang-Mills theory on 4-manifolds X of b1 (X) > 0, b2+ (X) = 1. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with b1 (X) > 0, b2+ (X) > 0. Explicit expressions for X = ℂ P1 × Fg, where Fg is a Riemann surface of genus g are obtained using Kronecker's double series identity. The result might be useful in future studies of quantum cohomology.",

author = "Marcos Mari{\~n}o and Gregory Moore",

year = "1999",

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pages = "249--267",

journal = "Communications in Mathematical Physics",

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T1 - Donaldson invariants for non-simply connected manifolds

AU - Mariño, Marcos

AU - Moore, Gregory

PY - 1999

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N2 - We study Coulomb branch ("u-plane") integrals for N = 2 supersymmetric SU (2), SO (3) Yang-Mills theory on 4-manifolds X of b1 (X) > 0, b2+ (X) = 1. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with b1 (X) > 0, b2+ (X) > 0. Explicit expressions for X = ℂ P1 × Fg, where Fg is a Riemann surface of genus g are obtained using Kronecker's double series identity. The result might be useful in future studies of quantum cohomology.

AB - We study Coulomb branch ("u-plane") integrals for N = 2 supersymmetric SU (2), SO (3) Yang-Mills theory on 4-manifolds X of b1 (X) > 0, b2+ (X) = 1. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with b1 (X) > 0, b2+ (X) > 0. Explicit expressions for X = ℂ P1 × Fg, where Fg is a Riemann surface of genus g are obtained using Kronecker's double series identity. The result might be useful in future studies of quantum cohomology.

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -

Donaldson invariants for non-simply connected manifolds

Abstract

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