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  2. Cubulating spaces and groups; example sheet 1 Macarena Arenas ...

    https://www.dpmms.cam.ac.uk/~mcr59/index_files/examplesheet1.pdf
    29 Jan 2024: b b. bb. b. b. b. b. b b. b. b. ... b b. b. b. 6. Let Γ and L, respectively, be the graph and the link pictured below.
  3. Lent Term 2024 O. Randal-Williams II Algebraic Topology // ...

    https://www.dpmms.cam.ac.uk/~or257/teaching/IIAlgTop2024/Sheet4.pdf
    11 Jan 2024: Show that the linear map A : R2 R2 peserves theequivalence relation (a,b) (a′,b′) (aa′,bb′) Z2, and so induces a continuous map fAfrom the torus T to itself.
  4. Lent Term 2024 O. Randal-Williams II Algebraic Topology // ...

    https://www.dpmms.cam.ac.uk/study/II/AlgebraicTopology/2023-2024/Sheet4.pdf
    16 Jan 2024: Show that the linear map A : R2 R2 peserves theequivalence relation (a,b) (a′,b′) (aa′,bb′) Z2, and so induces a continuous map fAfrom the torus T to itself.
  5. A Brief Guide ToMathematical Writing This guide is intended ...

    https://www.dpmms.cam.ac.uk/~grw46/Writing_Guide.pdf
    11 Mar 2024: f(B) then y = f(a) for some a A andy = f(b) for some b B but then f(a) = y = f(b) so a = b A Band y ... A B), so f(A) f(B) f(A B) and the sets are equal asrequired.
  6. 23 May 2024: b B(OF ) whose discriminant is strongly (resp. weakly) divisible by I 2. ... 2. Let b B(Op) be an element with discriminant weakly divisible by p2.
  7. Scrapbook on Set Theory with a Universal Set Thomas ...

    https://www.dpmms.cam.ac.uk/~tef10/NFnotesredux.pdf
    14 Jul 2024: The last rule in the proof of A B C can only be a -R. ... B. So then theboolean ring B′ corresponding to B believes the ring formula φ′ corresponding.
  8. NUMBER FIELDS, LENT 2024 PÉTER P. VARJÚ Disclaimer,…

    https://www.dpmms.cam.ac.uk/~pv270/NumberFields.pdf
    8 Mar 2024: Indeed, the minimalpolynomial of a/b with gcd(a,b) = 1 is xa/b. ... OK =. {a b 1 m. 1/2. 2: a,b Z. }if m 1 mod 4.
  9. Part IB - Groups, Rings, and Modules

    https://www.dpmms.cam.ac.uk/~or257/teaching/notes/GRM.pdf
    31 Jan 2024: 12 H. Definition (Abelian group). A group G is abelian if a b = b a for all a,b G. ... ii) (a b)(b c) = (a b c). (iii) (a b)(c d) = (a c b)(a c d).
  10. Random Thoughts on Machines and Computability Thomas Forster January…

    https://www.dpmms.cam.ac.uk/~tef10/cam_only/blog.pdf
    29 Jan 2024: similarly. However there is no suggestion that the Aand the B can be reidentified across the units. ... has three evenlyspaced ‘a’s or ‘b’s, irrespective of how widely spaced they are?
  11. MAPPING CLASS GROUPS OF h-COBORDANT MANIFOLDS SAMUEL MUÑOZ-ECHÁNIZ…

    https://www.dpmms.cam.ac.uk/~sm2600/papers/Mapping%20class%20groups%20of%20h-cobordant%20manifolds.pdf
    5 Jun 2024: Appendix Bexplores the connection between Theorem B and the theory of Weiss–Williams [WW88]. ... 2.3.1]. The next two subsections are devoted to prove Theorem B.

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