Exotic smooth structures on topological fiber bundles II

Author:

Goette Sebastian,Igusa Kiyoshi

Abstract

We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension plus 3). Using a variation of the Dwyer-Weiss-Williams smoothing theory which we explain in a separate joint paper with Bruce Williams, we associate a homology class in the total space of the bundle to each exotic smooth structure and show that the image of this class in the homology of the base is the Poincaré dual of the relative higher Igusa-Klein (IK) torsion invariant. This answers the question, in the relative case, of which cohomology classes can occur as relative higher torsion classes.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference23 articles.

1. On the groups 𝐽(𝑋). IV;Adams, J. F.;Topology,1966

2. Equivalence of higher torsion invariants;Badzioch, Bernard;Adv. Math.,2011

3. Smooth parametrized torsion: a manifold approach;Badzioch, Bernard;Adv. Math.,2009

4. Families torsion and Morse functions;Bismut, Jean-Michel;Ast\'{e}risque,2001

5. Flat vector bundles, direct images and higher real analytic torsion;Bismut, Jean-Michel;J. Amer. Math. Soc.,1995

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3