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H1–semistability for projective groups

Published online by Cambridge University Press:  31 May 2016

INDRANIL BISWAS  and
MAHAN MJ
INDRANIL BISWAS
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India. e-mails: indranil@math.tifr.res.in; mahan@math.tifr.res.in
MAHAN MJ
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India. e-mails: indranil@math.tifr.res.in; mahan@math.tifr.res.in
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Abstract

We initiate the study of the asymptotic topology of groups that can be realised as fundamental groups of smooth complex projective varieties with holomorphically convex universal covers (these are called here as holomorphically convex groups). We prove the H1-semistability conjecture of Geoghegan for holomorphically convex groups. In view of a theorem of Eyssidieux, Katzarkov, Pantev and Ramachandran [EKPR], this implies that linear projective groups satisfy the H1-semistability conjecture.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 1 , January 2017 , pp. 89 - 100
Copyright
Copyright © Cambridge Philosophical Society 2016 

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