Metadata
Mathematics Undergraduate Create Hard
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Metadata

  • Subject

    Mathematics

  • Education level

    Undergraduate

  • Cognitive goals

    Create

  • Difficulty estimate

    Hard

  • Tags

    algebraic topology, CW-complex, homology, cohomology ring, cup product

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Design a finite CW-complex X with H_0(X) ≅ Z, H_1(X) ≅ Z/4Z, H_2(X) ≅ Z^2, and H_n(X)=0 for n≥3. Specify a concrete cell decomposition (numbers of cells and explicit attaching maps), compute the cellular chain complex to verify the homology groups, then compute the integral cohomology groups H^*(X; Z) and determine the cohomology ring structure under the cup product (identify generators, relations, and any torsion cup-products). Address any universal coefficient or extension issues and show complete computations using cellular (co)chains.
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Attempts
100
Average Score
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Mock data used for demo purposes.