7 citations · 19 across the 12 of their papers we have counts for
14 papers
A normal form for the Thin Flat Surfaces category
Jaime Herrera, Carmen Rovi
The category TFS of thin flat surfaces, introduced by Khovanov, Qi, and Rozansky, is a strict symmetric monoidal category whose morphisms are compact oriented surfaces with corners…
A Stable Distance Persistence Homology for Dynamic Bayesian Network Clustering
Will Bales, Carmen Rovi
Dynamic Bayesian networks (DBNs) are a widely used framework for modeling systems whose probabilistic structure evolves over time. Standard inference methods focus on local conditi…
Algebraic Structures in Microtonal Music
Veronica Flynn, Carmen Rovi
We will discuss how certain group theory structures are found in music theory. Western music splits the octave into 12 equal tones called half-steps. We can take this division furt…
Nested cobordisms, Cyl-objects and Temperley-Lieb algebras
Maxine E. Calle, Renee S. Hoekzema, Laura Murray +3
We introduce a discrete cobordism category for nested manifolds and nested cobordisms between them. A variation of stratified Morse theory applies in this case, and yields generato…
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…
Chain duality for categories over complexes
James F. Davis, Carmen Rovi
We show that the additive category of chain complexes parametrized by a finite simplicial complex forms a category with chain duality. This fact, never fully proven in the orig…
Cut and paste invariants of manifolds via algebraic K-theory
Renee S. Hoekzema, Mona Merling, Laura Murray +2
Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic -theory, and applying these tools…
Signature Cocycles on the Mapping Class Group and Symplectic Groups
Dave Benson, Caterina Campagnolo, Andrew Ranicki +1
Werner Meyer constructed a cocycle in which computes the signature of a closed oriented surface bundle over a surface, with fibre a surface of…
Relating Cut and Paste Invariants and TQFTs
Carmen Rovi, Matthew Schoenbauer
In this paper, we shall be concerned with a relation between TQFTs and cut and paste invariants introduced by Karras, Kreck, Neumann and Ossa. Cut and paste invariants, or SK invar…
Cohomology of symplectic groups and Meyer's signature theorem
Dave Benson, Caterina Campagnolo, Andrew Ranicki +1
Meyer showed that the signature of a closed oriented surface bundle over a surface is a multiple of , and can be computed using an element of $H^2(\mathsf{Sp}(2g, \mathbb{Z}),\m…
Hirzebruch -genera modulo of fiber bundles for odd integers
Carmen Rovi, Shoji Yokura
I. Hambleton, A. Korzeniewski and A. Ranicki proved that the signature of a fibre bundle of closed, connected, compatibly oriented PL manifolds is always multiplicative modulo 4. I…
The non-multiplicativity of the signature modulo 8 of a fibre bundle is an Arf-Kervaire invariant
Carmen Rovi
It was proved by Chern, Hirzebruch and Serre that the signature of a fibre bundle is multiplicative if the fundamental group of the base acts trivially on the cohomology ring of th…
The signature modulo 8 of fibre bundles
Carmen Rovi
This thesis is concerned with the residues modulo 4 and 8 of the signature of a 4k-dimensional oriented geometric Poincare complex. The Z_8-valued Brown-Kervaire invariant of Z_4-v…
Orbispaces and their Mapping Spaces via Groupoids: A Categorical Approach
Vesta Coufal, Dorette Pronk, Carmen Rovi +2
In this paper, we give an accessible introduction to the theory of orbispaces via groupoids. We define a certain class of topological groupoids, which we call orbigroupoids. Each o…