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Obstructions to Riemannian smoothings of locally CAT(0) manifolds

Sathaye, Bakul, Sathaye
http://rave.ohiolink.edu/etdc/view?acc_num=osu1531416481628579

Abstract Details

2018, Doctor of Philosophy, Ohio State University, Mathematics.
In this dissertation, we address the following two questions. 1. Construct new examples of closed manifolds that are locally CAT(0), but do not support a smooth Riemannian metric with non-positive curvature. We extend the methods of Davis-Januszkiewicz-Lafont and provide a new obstruction to Riemannian smoothing of a locally CAT(0) manifold. In particular, we construct examples of locally CAT(0) 4-manifolds that do not support any Riemannian metric with non-positive sectional curvature. Further, the universal cover of such a manifold satis fies the isolated flats condition and contains a collection of 2-dimensional flats with the property that their boundaries at in finity form non-trivial links. Further the individual flats are unknotted at in finity. 2. Are there examples of non-trivial links that are link homotopically trivial and whose proper sublinks are all trivial? Examples are known of links that are either homotopically trivial or whose proper sublinks are trivial. We give new examples of links that satisfy both these properties. We also suggest a way to obtain a general result for producing examples of links that are link homotopic but not isotopic to any given link. To prove this, we use the Whitehead doubles of Brunnian links.
Jean-Francois Lafont (Advisor)
107 p.
Mathematics
Geometric topology, Geometric group theory

Recommended Citations

Citations

  • Sathaye, Sathaye, B. (2018). Obstructions to Riemannian smoothings of locally CAT(0) manifolds [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531416481628579

    APA Style (7th edition)

  • Sathaye, Sathaye, Bakul. Obstructions to Riemannian smoothings of locally CAT(0) manifolds. 2018. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1531416481628579.

    MLA Style (8th edition)

  • Sathaye, Sathaye, Bakul. "Obstructions to Riemannian smoothings of locally CAT(0) manifolds." Doctoral dissertation, Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531416481628579

    Chicago Manual of Style (17th edition)

osu1531416481628579
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