Abstract
We discuss topological aspects of the electroweak sphaleron and its odd-parity deformations. We demonstrate that they are uniquely classified in terms of their odd or even-parity pure gauge field behavior at spatial infinity. Fermion level crossing occurs only for odd-parity configurations, which are topologically disconnected from the vacuum. They contribute to the high temperature unsuppressed baryon violating thermal transitions. Deformations with even-parity pure gauge behavior at spatial infinity are topologically trivial and do not mediate baryon number violation in the early universe.
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