Perturbative N=2 supersymmetric quantum mechanics and L-theory with complex coefficients

TL;DR

This paper develops a complex coefficient version of L-theory derived from 1|2-dimensional perturbative supersymmetric mechanics, linking geometric quantization methods to algebraic topology.

Contribution

It introduces a novel construction of L-theory with complex coefficients using perturbative supersymmetric mechanics, connecting physics and algebraic topology.

Findings

Identification of wrong-way maps with MSO-orientation in complex L-theory

Construction of L-theory with complex coefficients from geometric mechanics

Linking perturbative quantization to algebraic topology structures

Abstract

We construct L-theory with complex coefficients from the geometry of 1|2-dimensional perturbative mechanics. Methods of perturbative quantization lead to wrong-way maps that we identify with those coming from the MSO-orientation of L-theory tensored with the complex numbers.