Oriented hairy graphs and moduli spaces of curves

Andersson, Assar; Willwacher, Thomas; Zivkovic, Marko

doi:10.48550/arxiv.2005.00439

Cited by 2 publications

(8 citation statements)

References 12 publications

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“…, n}. Fix n + 2 general points in P 1 . Let G m act so that the coordinates of the points in S are multiplied by z and the rest are multiplied by z −1 , and let C be the closure of this G m -orbit.…”

Section: Proof Any Other Tautological Generator For H 2 (M G−hn+2hmentioning

confidence: 99%

“…The subcomplex where the non-isolated part has genus h can be written as a tensor product J ⋆ h,n ⊗ G (h ′ ,1) [−1], where h + h ′ = g and J ⋆ h,n is a graph complex perfectly analogous to X ⋆ h,n , except that each generator has exactly one ω decoration instead of two, and this ω-decoration must be part of a non-isolated component. 1 We then have a decomposition (37)…”

Section: Direct Summands With Marked Pointsmentioning

confidence: 99%

“…Lacking lower bounds on the dimension of A n , we omitted this summand from the statement of Theorem 1.6. Here the component with internal vertices is the generator of H 6 (G (3,1) ) W 0 H 6 c (M 3,1 ). The disjoint union of two isolated edges corresponds to the generator of H(J ⋆ 0,2 ) of Example 8.5.…”

Section: The Cohomology Of Jmentioning

confidence: 99%

“…By [28], we know that gr 2 H • c (M 3,2 ) Q ⊕ sgn 2 , supported in degree 8. Our computation shows that the summand sgn 2 is naturally identified with H(J ⋆ 0,2 ) ⊗ H(G (3,1) )[−1]. Next, we turn to the second summand in Theorem 1.6.…”

Section: The Cohomology Of Jmentioning

confidence: 99%

“…Theorem 1.1. For all g and n such that 2g + n ≥ 3 and (g, n) (1,1) there is an S n -equivariant isomorphism…”

Section: Introductionmentioning

confidence: 99%

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Weight two compactly supported cohomology of moduli spaces of curves

Payne¹,

Willwacher²

2021

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We study the weight 2 graded piece of the compactly supported rational cohomology of the moduli spaces of curves M g,n and show that this can be computed as the cohomology of a graph complex that is closely related to graph complexes arising in the study of embedding spaces. For n = 0, we express this cohomology in terms of W 0 H • c (M g ′ ,n ′ ) for g ′ ≤ g and n ′ ≤ 2, and thereby produce several new infinite families of nonvanishing unstable cohomology groups on M g , including the first such families in odd degrees. In particular, we show that dim H 4g−k (M g ) grows at least exponentially with g, for k ∈ {8,

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Section: Proof Any Other Tautological Generator For H 2 (M G−hn+2hmentioning

confidence: 99%

Section: Direct Summands With Marked Pointsmentioning

confidence: 99%

Section: The Cohomology Of Jmentioning

confidence: 99%

Section: The Cohomology Of Jmentioning

confidence: 99%

“…Theorem 1.1. For all g and n such that 2g + n ≥ 3 and (g, n) (1,1) there is an S n -equivariant isomorphism…”

Section: Introductionmentioning

confidence: 99%