A Step towards Computational Derived Algebraic Geometry: The RepHomology Package For Macaulay2
Guanyu Li
TL;DR
This paper introduces the RepHomology package for Macaulay2, enabling computation of representation homology for surfaces and link complements, advancing computational algebraic geometry techniques.
Contribution
The paper presents a new Macaulay2 package that computes representation homology for specific topological spaces, bridging computational methods with algebraic geometry.
Findings
Successfully computes representation homology of surfaces and link complements.
Provides algorithms for algebra and Lie algebra coefficient cases.
Enhances computational tools for algebraic geometry and topology.
Abstract
We introduce the \verb|Macaulay2| package \verb|RepHomology| for the computations of representation homology of certain spaces. The main methods implement computing the representation homology of surfaces (with group coefficients, and analogies with algebra and Lie algebra coefficients), and the representation homology of link complements.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications