Conformally invariant gauge fixed actions for 2-D topological gravity. (English) Zbl 0725.53071

It seems that topology has benefited more from the marriage between the precise science of topology and the phenomenological science of quantum field theory. As is a now familiar story, S. K. Donaldson discovered new invariants for four-manifolds with the help of the new science of topological quantum field theory. In the present work, the authors show that the Mumford invariants for moduli spaces of curves [D. Mumford, Arithmetic and geometry, Pap. dedic. I. R. Shafarevich, Vol. II: Geometry, Prog. Math. 36, 271-328 (1983; Zbl 0554.14008)] can be obtained from a gauge fixed action of a topological quantum field theory in two dimensions. The method bears remarkable similarity to that of S. K. Donaldson in discovering his famous invariants [for a recent description of the Donaldson invariants see S. K. Donaldson and P. B. Kronheimer, The geometry of four manifolds (Clarendon Press, Oxford) (1990)].


53C80 Applications of global differential geometry to the sciences
83C47 Methods of quantum field theory in general relativity and gravitational theory
58D27 Moduli problems for differential geometric structures


Zbl 0554.14008
Full Text: DOI


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