A new construction of lens spaces

Soumen Sarkar; Dong Youp Suh

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arXiv · 1304.4836

A new construction of lens spaces

Soumen Sarkar·Dong Youp Suh

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Abstract

Let $T^n$ be the real $n$-torus group. We give a new definition of lens spaces and study the diffeomorphic classification of lens spaces. We show that any $3$-dimensional lens space $L(p; q)$ is $T^2$-equivariantly cobordant to zero. We also give some sufficient conditions for higher dimensional lens spaces $L(p; q_1, \ldots, q_n)$ to be $T^{n+1}$-equivariantly cobordant to zero. In 2005, B. Hanke showed that complex equivariant cobordism class of a lens space is trivial. Nevertheless, our proofs are constructive using toric topological arguments.

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BibTeX RIS

Soumen Sarkar, Dong Youp Suh. 2013-04-17. A new construction of lens spaces. https://arxiv.org/abs/1304.4836

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