标题： 参数化剪切合同 $K$-理论与流形和cobordism范畴 显示英文标题

标题： Parametrized scissors congruence $K$-theory of manifolds and cobordism categories

摘要： 我们构建了流形的剪切相容性$K$理论的参数化版本，这特别给出了定向流形的剪切相容性$K$理论的拓扑化版本，并我们将这个谱描述为在余 bordism 范畴和空间的通常代数$K$理论之间起中介作用。 我们在$\pi_0$上表明，定向流形的剪切相容性$K$理论与允许自由边界的一种余 bordism 范畴版本是一致的。 显示英文摘要

摘要： We construct a parametrized version of scissors congruence $K$-theory of manifolds, which in particular gives a topologized version of the scissors congruence $K$-theory of oriented manifolds, and we describe this spectrum as mediating between the cobordism category and usual algebraic $K$-theory of spaces. We show that on $\pi_0$, the scissors congruence $K$-theory of oriented manifolds agrees with a version of the cobordism category where we allow free boundaries.