nLab Manuel Rivera

• algebraic topology

• institute page

• MathGenealogy page

• GoogleScholar page

Selected writings

On Hochschild cohomology and string topology:

• Manuel Rivera, Zhengfang Wang: Singular Hochschild cohomology and algebraic string operations, Journal of Noncommutative Geometry 13 1 (2017) 297–361 [doi;10.4171/jncg/325]

On the homotopy type of free loop spaces:

• Manuel Rivera, Samson Saneblidze: A combinatorial model for the free loop space fibration, Bull. London Math. Soc. 50 (2018) 1085-1101 [doi:10.1112/blms.12202, arXiv:1712.02644]

Identifying the cobar construction on singular chains on a topological space with the dg-algebra of chains on its loop space:

• Manuel Rivera, Mahmoud Zeinalian, Cubical rigidification, the cobar construction, and the based loop space, Algebr. Geom. Topol. 18 (2018) 3789-3820 [arXiv:1612.04801, doi:10.2140/agt.2018.18.3789]

The weak homotopy equivalences among path connected pointed topological spaces can be detected by singular chain functor $C_*$, provided $C_*(X)$ is regarded its structure of a dg-coalgebra:

• Manuel Rivera, Felix Wierstra, Mahmoud Zeinalian: The functor of singular chains detects weak homotopy equivalences, Proc. Amer. Math. Soc. 147 (2019) 4987–4998 [doi:10.1090/proc/14555, arXiv/1807.06410, MR4011530]

On $\infty$-local systems in the sense of $(\infty,1)$-vector bundles with flat $\infty$-connections:

• Manuel Rivera, Mahmoud Zeinalian, §5 of: The colimit of an $\infty$-local system as a twisted tensor product, Higher Structures 4 1 (2020) 33-56 [arXiv:1805.01264, higher-structures:Vol4Iss1]

On rational homotopy theory for possibly non-nilpotent spaces via deck-Borel-equivariant rational homotopy theory:

• Manuel Rivera, Felix Wierstra, Mahmoud Zeinalian, Rational homotopy equivalences and singular chains, Algebr. Geom. Topol. 21 (2021) 1535-1552 [arXiv:1906.03655. doi:10.2140/agt.2021.21.1535]

Relating the Dwyer-Kan loop groupoid-construction to the homotopy coherent nerve-construction:

• Emilio Minichiello, Manuel Rivera, Mahmoud Zeinalian, Categorical models for path spaces, Advances in Mathematics 415 (2023) 108898 [arXiv:2201.03046, doi:10.1016/j.aim.2023.108898]

category: people