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arxiv: 2305.12548 · v3 · pith:YPM7BFOO · submitted 2023-05-21 · math.GT

The acyclicity of the complex of homologous curves

Daniel Minahan This is my paper

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classification math.GT
keywords complexcurveshomologousacyclicacyclicityclosedgenusoriented
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We show that the complex of homologous curves of a closed, oriented surface of genus g is (g-3)--acyclic.

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  1. Finite generation, algebraicity, and representation stability for homology of Torelli groups

    math.GT 2026-06 unverdicted novelty 8.0

    Proves finite generation of H_k(I_g; Z) for k ≤ g-2 and that rational homology is an algebraic Sp(2g,Z)-representation, turning conditional cohomology computations into theorems and proving Morita's conjecture.