caa a22 4500 445884568 CHVBK 20180317145555.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10711-010-9508-5 doi (NATIONALLICENCE)springer-10.1007/s10711-010-9508-5 Morse theory of the moment map for representations of quivers [Elektronische Daten] [Megumi Harada, Graeme Wilkin] The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-Hölder filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts. Springer Science+Business Media B.V., 2010 Hyperkähler quotient nationallicence Quiver variety nationallicence Equivariant cohomology nationallicence Morse theory nationallicence Harada Megumi Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut Wilkin Graeme Department of Mathematics, University of Colorado, 80309-0395, Boulder, CO, USA aut Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 307-353 0046-5755 150:1<307 2011 150 10711 https://doi.org/10.1007/s10711-010-9508-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9508-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Harada Megumi Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada aut NATIONALLICENCE 700 1- Wilkin Graeme Department of Mathematics, University of Colorado, 80309-0395, Boulder, CO, USA aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 307-353 0046-5755 150:1<307 2011 150 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer