Characteristic classes of moduli spaces— Riemann surface, graph, homology cobordism

2020 ◽  
Vol 33 (2) ◽  
pp. 197-222
Author(s):  
Shigeyuki Morita
Keyword(s):  
Riemann Surface ◽  
Moduli Spaces ◽  
Characteristic Classes ◽  
Surface Graph ◽  
Graph Homology ◽  
Homology Cobordism

scholarly journals Twisted orbifold Gromov–Witten invariants

2014 ◽  
Vol 213 ◽  
pp. 141-187 ◽  
Author(s):  
Valentin Tonita
Keyword(s):  
Moduli Spaces ◽  
Compact Manifold ◽  
Characteristic Classes ◽  
Stable Maps ◽  
Fundamental Class ◽  
Generating Series

AbstractLet χ be a smooth proper Deligne–Mumford stack over ℂ. One can define twisted orbifold Gromov–Witten invariants of χ by considering multiplicative invertible characteristic classes of various bundles on the moduli spaces of stable maps χg,n,d, cupping them with evaluation and cotangent line classes, and then integrating against the virtual fundamental class. These are more general than the twisted invariants introduced by Tseng. We express the generating series of the twisted invariants in terms of the generating series of the untwisted ones. We derive the corollaries which are used in a paper with Givental about the quantum K-theory of a complex compact manifold X.

scholarly journals Intersection pairings on singular moduli spaces of bundles over a Riemann surface and their partial desingularisations

2006 ◽  
Vol 11 (3) ◽  
pp. 439-494
Author(s):  
Lisa Jeffrey ◽  
Young-Hoon Kiem ◽  
Frances C. Kirwan ◽  
Jonathan Woolf
Keyword(s):  
Riemann Surface ◽  
Moduli Spaces ◽  
Singular Moduli

scholarly journals CHEN–RUAN COHOMOLOGY OF SOME MODULI SPACES, II

2010 ◽  
Vol 21 (04) ◽  
pp. 497-522 ◽  
Author(s):  
INDRANIL BISWAS ◽  
MAINAK PODDAR
Keyword(s):  
Riemann Surface ◽  
Line Bundle ◽  
Prime Number ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Vector Bundles ◽  
Line Bundles ◽  
Holomorphic Line Bundle ◽  
Stable Vector Bundles

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and ξ → X a holomorphic line bundle such that r is not a divisor of degree ξ. Let [Formula: see text] denote the moduli space of stable vector bundles over X of rank r and determinant ξ. By Γ we will denote the group of line bundles L over X such that L⊗r is trivial. This group Γ acts on [Formula: see text] by the rule (E, L) ↦ E ⊗ L. We compute the Chen–Ruan cohomology of the corresponding orbifold.

scholarly journals GEOMETRY OF MODULI SPACES OF FLAT BUNDLES ON PUNCTURED SURFACES

1998 ◽  
Vol 09 (01) ◽  
pp. 63-73 ◽  
Author(s):  
PHILIP A. FOTH
Keyword(s):  
Riemann Surface ◽  
Conjugacy Class ◽  
Moduli Spaces ◽  
Flat Connections ◽  
Rational Singularities ◽  
Take All

For a Riemann surface with one puncture we consider moduli spaces of flat connections such that the monodromy transformation around the puncture belongs to a given conjugacy class with the property that a product of its distinct eigenvalues is not equal to 1 unless we take all of them. We prove that these moduli spaces are smooth and their natural closures are normal with rational singularities.

scholarly journals Twisted orbifold Gromov–Witten invariants

2014 ◽  
Vol 213 ◽  
pp. 141-187
Author(s):  
Valentin Tonita
Keyword(s):  
Moduli Spaces ◽  
Compact Manifold ◽  
Characteristic Classes ◽  
Stable Maps ◽  
Fundamental Class ◽  
Generating Series

AbstractLetχbe a smooth proper Deligne–Mumford stack over ℂ. One can define twisted orbifold Gromov–Witten invariants ofχby considering multiplicative invertible characteristic classes of various bundles on the moduli spaces of stable mapsχg,n,d, cupping them with evaluation and cotangent line classes, and then integrating against the virtual fundamental class. These are more general than the twisted invariants introduced by Tseng. We express the generating series of the twisted invariants in terms of the generating series of the untwisted ones. We derive the corollaries which are used in a paper with Givental about the quantumK-theory of a complex compact manifoldX.

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