Periodic points and topological restriction homology
1 hour 2 mins,
114.03 MB,
MP3
44100 Hz,
251.11 kbits/sec
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Description: |
Malkiewich, C
Wednesday 5th December 2018 - 09:00 to 10:00 |
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Created: | 2018-12-05 15:48 |
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Collection: | Higher structures in homotopy theory |
Publisher: | Isaac Newton Institute |
Copyright: | Malkiewich, C |
Language: | eng (English) |
Distribution: | World (downloadable) |
Explicit content: | No |
Aspect Ratio: | 16:9 |
Screencast: | No |
Bumper: | UCS Default |
Trailer: | UCS Default |
Abstract: | I will talk about a project to import trace methods, usually reserved for algebraic K-theory computations, into the study of periodic orbits of continuous dynamical systems (and vice-versa). Our main result so far is that a certain fixed-point invariant built using equivariant spectra can be "unwound" into a more classical invariant that detects periodic orbits. As a simple consequence, periodic-point problems (i.e. finding a homotopy of a continuous map that removes its n-periodic orbits) can be reduced to equivariant fixed-point problems. This answers a conjecture of Klein and Williams, and allows us to interpret their invariant as a class in topological restriction homology (TR), coinciding with a class defined earlier in the thesis of Iwashita and separately by Luck. This is joint work with Kate Ponto.
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