nLab Manuel Rivera

• webpage

Selected writings

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]

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]

See also:

• M. Rivera, and S. Saneblidze, A combinatorial model for the free loop space fibration, Bull. London Math. Soc. (2018) doi:10.1112/blms.12202, arXiv:1712.02644

• M. Rivera, F. Wierstra, M. Zeinalian, The functor of singular chains detects weak homotopy equivalences, Proc. Amer. Math. Soc. (2019) arXiv:1808.10237

• M. Rivera and Z. Wang, Singular Hochschild cohomology and algebraic string operations, J. Noncommut. Geom. 13 (2019), 297-361.arXiv:1703.03899

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