scholarly journals Compactifying Torus Fibrations Over Integral Affine Manifolds with Singularities

2021 ◽  
pp. 609-622 ◽  
Author(s):  
Helge Ruddat ◽  
Ilia Zharkov
Keyword(s):  
Affine Manifolds ◽  
Manifolds With Singularities

scholarly journals Topology of Subvarieties of Complex Semi-abelian Varieties

2020 ◽  
Author(s):  
Yongqiang Liu ◽  
Laurentiu Maxim ◽  
Botong Wang
Keyword(s):  
Euler Characteristic ◽  
Morse Theory ◽  
Characteristic Property ◽  
Abelian Varieties ◽  
Betti Numbers ◽  
Local Systems ◽  
Affine Manifolds ◽  
Cyclic Covers ◽  
Rank One ◽  
Generic Vanishing

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.

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):  
Affine Manifolds

The Mixed Scalar Curvature of Almost-Product Metric-Affine Manifolds

2018 ◽  
Vol 73 (1) ◽  
Author(s):  
Vladimir Rovenski ◽  
Tomasz Zawadzki
Keyword(s):  
Scalar Curvature ◽  
Affine Manifolds

scholarly journals Self-affine manifolds

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