Infinite symmetric group and bordisms of pseudomanifolds

Abstract

We consider a category whose morphisms are bordisms of $n$-dimensional pseudomanifolds equipped with a certain additional structure (coloring). On the other hand, we consider the product $G$ of $(n+1)$ copies of infinite symmetric group. We show that unitary representations of $G$ produce functors from the category of $(n-1)$-dimensional bordisms to the category of Hilbert spaces and bounded linear operators.

14pp

References in corpus (3)

• Universal Realisators for Homology Classes
• Combinatorial realisation of cycles and small covers
• A remark on representations of infinite symmetric groups

Cited by in corpus (2)

• Multiplication of conjugacy classes, colligations, and characteristic functions of matrix argument
• On the group of infinite $p$-adic matrices with integer elements