The Witten-Reshetikhin-Turaev invariant for links in finite order mapping tori I

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• 作者：Jø ; rgen Ellegaard Andersen^a ; ¹ ; ² ; ^{andersen@qgm.au.dk" class="auth_mail" title="E-mail the corresponding author} ; Benjamin Himpel^a ; ¹ ; ^{himpel@qgm.au.dk" class="auth_mail" title="E-mail the corresponding author} ; ^{himpel@uni-bonn.de" class="auth_mail" title="E-mail the corresponding author} ; Sø ; ren Fuglede Jø ; rgensen^b ; ¹ ; ³ ; ^{s@fuglede.dk" class="auth_mail" title="E-mail the corresponding author} ; Johan Martens^c ; ¹ ; ² ; ^{johan.martens@ed.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Brendan McLellan^d ; ¹ ; ^{mclellan@math.harvard.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Witten&ndash ; Reshetikhin&ndash ; Turaev link invariants ; Chern&ndash ; Simons theory ; TQFT ; Gauge theory ; Asymptotic expansion conjecture ; Growth rate conjecture
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：2 January 2017
• 年：2017
• 卷：304
• 期：Complete
• 页码：131-178
• 全文大小：835 K

文摘

We state Asymptotic Expansion and Growth Rate conjectures for the Witten–Reshetikhin–Turaev invariants of arbitrary framed links in 3-manifolds, and we prove these conjectures for the natural links in mapping tori of finite-order automorphisms of marked surfaces. Our approach is based upon geometric quantisation of the moduli space of parabolic bundles on the surface, which we show coincides with the construction of the Witten–Reshetikhin–Turaev invariants using conformal field theory, as was recently completed by Andersen and Ueno.