- 5. The universal surface bundle over the Torelli space has no sections. Arxiv For g>3, we give two proofs of the fact that the Birman exact sequence for the Torelli group does not split.
- 4. Section problems for configuration spaces of surfaces. Arxiv In this paper we give a close-to-sharp answer to the basic questions:
- 3. Surjective homomorphisms between surface braid groups. Arxiv Notes Classify surjective homomorphisms from PB_n(S_g,p) to PB_m(S_g,p), n-strand braid group to m-strand braid group.
- 2. The number of fiberings of a surface bundle over a surface. Arxiv Compute the number of ways Atiyah Kodaira example can fiber over a surface.
- 1. The universal n-pointed surface bundle only has n sections. Arxiv Classify homomorphisms from PB_n(S_g) to Pi_1(S_g), n-strand braid group to 1-strand braid group.

We also prove that the universal n-pointed Torelli bundle only has n sections up to homotopy. (2017)

submitted

When is there a continuous way to add a point to a configuration of n ordered points on a surface S of finite type so that all the points are still distinct?

We will answer the question for R^2, S^2 and S_g when g>1.(2017)

Submitted.

Then we compute the automorphism group of PB_n(S_g,p)

Surprisingly, in contrast to the n=1 case, any automorphism of PB_n(S_g,p), n>1 is geometric.(2017)

Submitted.

We also compute the fibering number of some other examples. (2017)

Submitted.

Using this, we classify sections of the universal n-pointed surface bundle and the universal n-pointed hyper-elliptic surface bundle. (2016)

Accepted by Journal of Topology and Analysis.

In Winter 2014 I passed my topic exam, on Characteristic Classes of Surface Bundles, under the supervision of Benson Farb. The proposal is here.

- 2. ICMS Edinburgh Slides: Surjective homomorphisms between surface braid groups.
- 1. Oberwalfach surface bundle Youtube video: The section problems.

Notes: The section problems

small lucky

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close to you

- In the 2016-2017 school year, I taught Calculus 151-131-132.
- In the 2015-2016 school year, I taught Calculus 151-152-153.
- In the 2014-2015 school year, I was a College Fellow for IBL Calculus 161-162-163. Teaching Advisor: Sarah Ziesler

sziesler at uchicago.edu

I'm a graduate student in at The University of Chicago, interested in Mapping Class Group and topology in general.

5734 S. University Avenue

Chicago, IL 60637-1514

USA

Chicago, IL 60637-1514

USA

chenlei1991919@gmail.com | |

Office | E105 in Eckhart |

Advisor | Benson Farb |

Here | is my CV |