scholarly journals Horizontal Holonomy for Affine Manifolds

2015 ◽  
Vol 22 (3) ◽  
pp. 413-440
Author(s):  
Boutheina Hafassa ◽  
Amina Mortada ◽  
Yacine Chitour ◽  
Petri Kokkonen
Keyword(s):  
Author(s):  
Yongqiang Liu ◽  
Laurentiu Maxim ◽  
Botong Wang

Abstract We use the non-proper Morse theory of Palais–Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties and that of their infinite cyclic covers. As main applications, we obtain the finite generation (except in the middle degree) of the corresponding integral Alexander modules as well as the signed Euler characteristic property and generic vanishing for rank-one local systems on such subvarieties. Furthermore, we give a more conceptual (topological) interpretation of the signed Euler characteristic property in terms of vanishing of Novikov homology. As a byproduct, we prove a generic vanishing result for the $L^2$-Betti numbers of very affine manifolds. Our methods also recast June Huh’s extension of Varchenko’s conjecture to very affine manifolds and provide a generalization of this result in the context of smooth closed sub-varieties of semi-abelian varieties.


2018 ◽  
Vol 73 (1) ◽  
Author(s):  
Vladimir Rovenski ◽  
Tomasz Zawadzki

2016 ◽  
Vol 289 ◽  
pp. 725-783 ◽  
Author(s):  
Gregory R. Conner ◽  
Jörg M. Thuswaldner
Keyword(s):  

1977 ◽  
Vol 29 (1) ◽  
pp. 135-149 ◽  
Author(s):  
Yusuke SAKANE
Keyword(s):  

Author(s):  
Agata Smoktunowicz

In 2014, Wolfgang Rump showed that there exists a correspondence between left nilpotent right [Formula: see text]-braces and pre-Lie algebras. This correspondence, established using a geometric approach related to flat affine manifolds and affine torsors, works locally. In this paper, we explain Rump’s correspondence using only algebraic formulae. An algebraic interpretation of the correspondence works for fields of sufficiently large prime characteristic as well as for fields of characteristic zero.


1980 ◽  
Vol 3 (3) ◽  
pp. 1045-1048 ◽  
Author(s):  
D. Fried ◽  
W. Goldman ◽  
M. W. Hirsch

Sign in / Sign up

Export Citation Format

Share Document