Julia Semikina

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20242026

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math.AT2026

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

Mona Merling, George Raptis, Julia Semikina

We introduce a parametrized version of scissors congruence $K$ -theory of manifolds with tangential structure, which includes a topologized version of the scissors congruence $K$ -th…

math.AT2025

Scissors congruence K-theory for equivariant manifolds

Mona Merling, Ming Ng, Julia Semikina +2

We introduce a scissors congruence $K$ -theory spectrum which lifts the equivariant scissors congruence groups for compact $G$ -manifolds with boundary, and we show that on $I ¨ _{0}$ th…

math.AT2024

A K-theory spectrum for cobordism cut and paste groups

Renee S. Hoekzema, Carmen Rovi, Julia Semikina

Cobordism groups and cut-and-paste groups of manifolds arise from imposing two different relations on the monoid of manifolds under disjoint union. By imposing both relations simul…

Parametrized scissors congruence K-theory of manifolds and cobordism categories

Scissors congruence K-theory for equivariant manifolds

A K-theory spectrum for cobordism cut and paste groups

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