# Virtual vector bundles and graded Thom spectra

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## Abstract

We introduce a convenient framework for constructing and analyzing orthogonal Thom spectra arising from virtual vector bundles. This framework enables us to set up a theory of orientations and graded Thom isomorphisms with good multiplicative properties. The theory is applied to the analysis of logarithmic structures on commutative ring spectra.

## Notes

### Acknowledgements

The authors would like to thank the referee for useful comments on the paper.

## References

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