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22 Aug 2023: Theorem 2.1.20 ([Hag08]). If ϕ : Y X is a local isometry, then:. ... Proof. One direction follows from Theorem 2.1.36, together with the π1-injectivity of localisometries stated in Theorem 2.1.20.

14 Sep 2023: c) Choose an arbitrary point x X. Since X is finite, M(X,Z) is isomorphic tothe (co)induced module IndGxG Z in the sense of [20, Chapter I, 6], where ... Thus. 20 KONSTANTIN ARDAKOV AND SIMON WADSLEY. by Proposition 3.1.4 again we can deduce that [L ] =

24 Oct 2023: Lemma 6.20. 1. If χ is an (irreducible) character, then so is χ̄. ... 20. 6.4 First projection formulaLecture 6starts here. We will now work our way towards proving Theorem 6.7.

10 Feb 2023: simple descriptions in terms of the homologyand Laplacian of a generalized reduced dual graph (Corollary 1.20). ... There has been considerable interest in “Jacobians of graphs” — for example, Lorenzini[19, 20], Bacher–de la Harpe–Nagnibeda [1]

10 Oct 2023: Example sheet 1 updated 20 Oct 2010.

21 Nov 2023: Singularities and cosmic censorship in general relativity, Infinities and Cosmology, DAMTP, Cambridge, 19 and 20 March 2013.

12 Jan 2023: Example 2.20 (continuing 2.16). (i) Let G = PSL2(Z) y H2, and let. ... 20. are constants K,C, such that for all a,b MCG(S),. dMCG(S)(a,b) K,CYS.

1 Feb 2023: What is. it?We have dK = 20 so can take c =. 80π< 9. π< 3. So every ideal class contains. an ideal of norm 2. ... x1x2 = R. (Picture). 20. So apply Minkowski’s theorem, we need to choose a convex symmetric setcontained in this region.

20 Dec 2023: Theseresults further support the ‘rigid-analytic quantisation’ intuition: more general pre-cise conjectures in the direction of this philosophy can be found at [20, Chapter 5].The proofs in Chapter 3 ... 20 KONSTANTIN ARDAKOV AND SIMON WADSLEY. The

9 Nov 2023: A WEISS–WILLIAMS THEOREM FOR SPACES OF EMBEDDINGSAND THE HOMOTOPY TYPE OF SPACES OF LONG KNOTS. SAMUEL MUÑOZ-ECHÁNIZ. ABSTRACT. We establish a pseudoisotopy result for embedding spaces in the line of that of Weiss and Williamsfor