The classifying space of hBord_2 is rationally equivalent to a circle, while B(hBord_2^{χ≤0}) has rational homotopy groups containing the homology of all moduli spaces of tropical curves Δ_g as a summand, via positive boundary surgery on labelled cospan categories.
arXiv:1604.03176 , Title =
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abstract
We study the topology of the tropical moduli space parametrizing stable tropical curves of genus g with n marked points in which the bounded edges have total length 1, and prove that it is highly connected. Using the identification of this space with the dual complex of the boundary in the moduli space of stable algebraic curves, we give a simple expression for the top weight cohomology of M_{1,n} as a representation of the symmetric group and describe an explicit dual basis in homology consisting of abelian cycles for the pure mapping class group.
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UNVERDICTED 2representative citing papers
The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.
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The surface category and tropical curves
The classifying space of hBord_2 is rationally equivalent to a circle, while B(hBord_2^{χ≤0}) has rational homotopy groups containing the homology of all moduli spaces of tropical curves Δ_g as a summand, via positive boundary surgery on labelled cospan categories.
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The integral Chow ring of $\mathscr{M}_{0}(\mathbb{P}^r, 2)$
The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.