Publications and preprints

• Koszul duality and Calabi-Yau structures, J. Holstein, M. Rivera, submitted, arXiv:2410.03604

• Cyclic homology of categorical coalgebras and the free loop space, submitted, M. Rivera, D. Tolosa, arXiv:2403.08116 

• Algebraic string topology from the neighborhood of infinity, submitted, M. Rivera, A. Takeda, Z. Wang, arXiv:2308.09684

• A detailed look at the Szczarba map, E. Minichiello, M. Rivera, M. Zeinalian, arXiv:2305.13638

• The simplicial coalgebra of chains under three different notions of weak equivalence, G. Raptis, M. Rivera, IMRN, no. 16, 11766-11811 (2024). arXiv:2206.06335

• Adams’ cobar construction as a monoidal E-infinity coalgebra model of the based loop space,  A. Medina-Mardones, M. Rivera, Forum Math. Sigma 12 (2024) arXiv:2108.02790

• An algebraic model for the free loop space, M. Rivera, Higher Structures in Geometry, Topology and Physics, 23-47, Contemp. Math., 802, Amer. Math. Soc., Providence, RI (2024). arXiv:2210.10096

• Categorical models for path spaces,  E. Minichello, M. Rivera, M. Zeinalian, Adv. Math. 415 (2023)  arXiv:2201.03046

• String topology in three flavours, F. Naef, M. Rivera, N. Wahl, EMS Surv. Math. Sci. 10 (2023), no. 2, 243–305 [Dennis Sullivan’s 80th birthday volume] arXiv:2203.02429

• Adams’ cobar construction revisited, M. Rivera, Doc. Math. 27, 1213-1223 (2022), arXiv:1910.08455

• Invariance of the Goresky-Hingston algebra on reduced Hochschild homology, M. Rivera, Z. Wang, Proc. London Math. Soc., 125 (2022), 219-257. arXiv:1912.13267

• The simplicial coalgebra of chains determines homotopy types rationally and one prime at a time, M. Rivera, F. Wierstra, M. Zeinalian, Trans. Amer. Math. Soc. 375 (2022), no. 5, 3267–3303. arXiv:2006.05362

• Rational homotopy equivalences and singular chains, M. Rivera, F. Wierstra, M. Zeinalian, Algebr. Geom. Topol. 21 (2021), no. 3, 1535-1552. arXiv:1906.03655

• Singular chains and the fundamental group, M. Rivera, M. Zeinalian, Fund. Math. 253 (2021), no. 3, 297-316. arXiv:1801.06410

• The colimit of an infinity local system as a twisted tensor product, M. Rivera, M. Zeinalian, High. Struct. 4 (2020), no. 1, 33-56. arXiv:1805.01264

• The functor of singular chains detects weak homotopy equivalences, M. Rivera, F. Wierstra, M. Zeinalian, Proc. Amer. Math. Soc. 147 (2019), no. 11, 4987-4998. arXiv:1808.10237

• Singular Hochschild cohomology and algebraic string operations, M. Rivera, Z. Wang, J. Noncommut. Geom. 13 (2019), no. 1, 297-361. arXiv:1703.03899

• A combinatorial model for the path fibration, M. Rivera, S. Saneblidze, J. Homotopy Relat. Struct. 14 (2019), no. 2, 393-410. arXiv:1706.00983

• Cubical rigidification, the cobar construction, and the based loop space, M. Rivera, M. Zeinalian, Algebr. Geom. Topol. 18 (2018), no. 7, 3789-3820. arXiv:1612.04801

• A combinatorial model for the free loop space fibration, M. Rivera, S. Saneblidze, Bull. Lond. Math. Soc. 50 (2018), no. 6, 1085-1101. arXiv:1712.02644

• Automorphism groups of countably categorical linear orders are extremely amenable, F. Dorais, S. Gubkin, D. McDonald, M. Rivera, Order 30 (2013), 415–426. arXiv:1202.4092

Miscellaneous

• Teoría de homotopía usando conjuntos simpliciales, M. Campillo, A. Osorno, M. Rivera, arXiv:2411.10567

• Cibercoloquio Latinoamericano de Matemáticas, D. Campos, M. Rivera, M.A. Salazar, J. Samper, J. Simental, S. Villar, Notices Amer. Math. Soc. 68 (2021), no. 5, 793–797

• Summary of Chen’s theory of iterated integrals and the (co)homology of the based loop space

• Chen’s power series connection

• Toronto Spaces, The Harvard College Mathematics Review 3 (2011) 24-27