# 4th Geometry Festival, Budapest

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1978. [13] Hitchin, Nigel. Lectures on special Lagangian submanifolds. In Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999), volume 23 of AMS/IP Stud. Adv. , pages 151–182. Amer. Math. , Providence, RI, 2001. [14] Hopkins, Michael J. and Jeffrey H. Smith. Nilpotence and stable homotopy theory. II. Ann. of Math. (2), 148(1): 1–49, 1998. [15] Kapranov, M. M. and V. A. Voevodsky. 2-categories and Zamolodchikov tetrahedra equations. In Algebraic Groups and Their Generalizations: Quantum and Infinite-Dimensional Methods (University Park, PA, 1991), volume 56 of Proc.

2. Let E(d) = EU (d) ×U (d) Cd ↓ BU (d) be the universal Cd bundle over BU (d). There is a universal n × n matrix E = (E i j )i,n j=1 32 Baas, Dundas and Rognes of Hermitian vector bundles over |G L n (V)|. Over the path component n |G L n (V) D | = BU (di j ) i, j=1 for D = (di j )i,n j=1 in G L n (N), the (i, j)th entry in E is the pullback of the universal bundle E(di j ) along the projection |G L n (V) D | → BU (di j ). Let |Ar U (d)| be the geometric realization of the arrow category Ar U (d), where U (d) is viewed as a topological groupoid with one object.

29] Shimada, Nobuo and Kazuhisa Shimakawa. Delooping symmetric monoidal categories. Hiroshima Math. , 9(3): 627–645, 1979. [30] Suslin, A. On the K -theory of algebraically closed fields. Invent. , 73(2): 241–245, 1983. [31] Thomason, R. W. Homotopy colimits in the category of small categories. Math. Proc. Cambridge Philos. , 85(1): 91–109, 1979. [32] Thomason, R. W. Beware the phony multiplication on Quillen’s a −1 a. Proc. Amer. Math. , 80(4): 569–573, 1980. [33] Waldhausen, Friedhelm. Algebraic K -theory of topological spaces.