New York Journal of Mathematics
Volume 24 (2018), 443-450


Hemanth Saratchandran

Finite volume hyperbolic complements of 2-tori and Klein bottles in closed smooth simply connected 4-manifolds

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Published: August 7, 2018
Keywords: Hyperbolic 4-manifolds, link complements in simply connected closed smooth 4-manifolds.
Subject: 57M50, 57Q45.

We give necessary conditions, for a closed smooth simply connected 4-manifold X, to contain a collection of surfaces L such that X-L admits a complete finite volume hyperbolic structure. We then show that examples of non-compact hyperbolic 4-manifolds constructed by Ivanšić, and Ivanšić, Ratcliffe and Tschantz, give rise to examples of such link complements in #2kS2 x S2.


The author thanks Andras Juhasz, Marc Lackenby, and John Parker for their valuable comments on an earlier version of this work. A thanks must also be given to Igor Belegradek for providing a useful reference on eta invariants. Finally, the author wishes to thank the referees for their comments and corrections to the paper.

Author information

Hemanth Saratchandran:
Beijing International Center for Mathematical Research, No. 5 Yiheyuan Road, Haidian District, Beijing 100871, China P.R.