Đại số đồng điều coHochschild và đồng điều của không gian vòng tự do

Aguiar, M., Mahajan, S.: Monoidal Functors, Species and Hopf Algebras, Volume 29 of CRM Monograph Series. American Mathematical Society, Providence (2010) (With forewords by Kenneth Brown and Stephen Chase and André Joyal) Angeltveit, V., Rognes, J.: Hopf algebra structure on topological Hochschild homology. Algebr. Geom. Topol. 5, 1223–1290 (2005) Bayındır, H., Péroux, M.: Spanier–Whitehead duality for topological coHochschild homology (2020). arXiv:math.AT/2012.03966 Bohmann, A.M., Gerhardt, T., Høgenhaven, A., Shipley, B., Ziegenhagen, S.: Computational tools for topological coHochschild homology. Topol. Appl. 235, 185–213 (2018) Bökstedt, M.: The topological Hochschild homology of \(\mathbb{Z}\) and \(\mathbb{Z}/p\)(unpublished) Bousfield, A.K., Kan, D.M.: Homotopy Limits, Completions and Localizations. Lecture Notes in Mathematics, vol. 304. Springer, Berlin (1972) Bousfield, A.K., Kan, D.M.: Pairings and products in the homotopy spectral sequence. Trans. Am. Math. Soc. 177, 319–343 (1973) Bousfield, A.K., Kan, D.M.: A second quadrant homotopy spectral sequence. Trans. Am. Math. Soc. 177, 305–318 (1973) Brzezinski, T., Wisbauer, R.: Corings and Comodules. London Mathematical Society Lecture Note Series, vol. 309. Cambridge University Press, Cambridge (2003) Burghelea, D., Fiedorowicz, Z.: Cyclic homology and algebraic \(K\)-theory of spaces. II. Topology 25(3), 303–317 (1986) Chas, M., Sullivan, D.: String topology (1999). arXiv:math.GT/9911159 Cohen, R.L., Jones, J.D.S.: A homotopy theoretic realization of string topology. Math. Ann. 324(4), 773–798 (2002) Cohen, R.L., Jones, J.D.S., Yan, J.: The loop homology algebra of spheres and projective spaces. In: Categorical Decomposition Techniques in Algebraic Topology (Isle of Skye, 2001), Volume 215 of Progress in Mathematics, pp. 77–92. Birkhäuser, Basel (2004) Doi, Y.: Homological coalgebra. J. Math. Soc. Jpn. 33(1), 31–50 (1981) Eilenberg, S., Moore, J.C.: Homology and fibrations. I. Coalgebras, cotensor product and its derived functors. Comment. Math. Helv. 40, 199–236 (1966) Elmendorf, A.D., Kriz, I., Mandell, M.A., May, J.P.: Rings, Modules, and Algebras in Stable Homotopy theory, volume 47 of Mathematical Surveys and Monographs. American Mathematical Society, Providence (1997) (with an appendix by M. Cole) Goodwillie, T.G.: Cyclic homology, derivations, and the free loopspace. Topology 24(2), 187–215 (1985) Gromoll, D., Meyer, W.: Periodic geodesics on compact riemannian manifolds. J. Differ. Geom. 3, 493–510 (1969) Hess, K., Parent, P.-E., Scott, J.: CoHochschild homology of chain coalgebras. J. Pure Appl. Algebra 213(4), 536–556 (2009) Hess, Kathryn, Shipley, Brooke: Invariance properties of coHochschild homology. J. Pure Appl. Algebra 225(2), 106505 (2021) Joyal, A.: Quasi-categories and Kan complexes. J. Pure Appl. Algebra 175(1–3), 207–222 (2002) Klanderman, S.: Computations of relative topological coHochschild homology. arXiv:2108.07863 (2021) Kuribayashi, K.: The Hochschild cohomology ring of the singular Cochain algebra of a space. Ann. Inst. Fourier (Grenoble) 61(5):1779–1805 (2012) (2011) Kuribayashi, K., Menichi, L., Naito, T.: Behavior of the Eilenberg–Moore spectral sequence in derived string topology. Topol. Appl. 164, 24–44 (2014) Kuribayashi, K., Yamaguchi, T.: The cohomology algebra of certain free loop spaces. Fund. Math. 154(1), 57–73 (1997) Lurie, J.: Elliptic cohomology I. September 2016 version. Available on author’s homepage Lurie, J.: Higher algebra. September 2017 version. Available on author’s homepage Malkiewich, C.: Cyclotomic structure in the topological Hochschild homology of \(DX\). Algebra Geom. Topol. 17(4), 2307–2356 (2017) McClure, J., Schwänzl, R., Vogt, R.: \(T\!H\!H(R)\cong R\otimes S^1\) for \(E_\infty \) ring spectra. J. Pure Appl. Algebra 121(2), 137–159 (1997) Menichi, L.: The cohomology ring of free loop spaces. Homol. Homotopy Appl. 3(1), 193–224 (2001) Péroux, M.: Rigidification of connective comodules (2020). arXiv:2006.09398 Riehl, E., Verity, D.: Elements of \(\infty \)-category theory. Version of May 2021. Available on the first author’s homepage Smith, L.: The Eilenberg–Moore spectral sequence and the mod \(2\) cohomology of certain free loop spaces. Ill. J. Math. 28(3), 516–522 (1984) Moss, E.: Sweedler. Hopf algebras. Mathematics Lecture Note Series. W. A. Benjamin Inc, New York (1969) Weibel, C.A.: An Introduction to Homological Algebra. Cambridge Studies in Advanced Mathematics, vol. 38. Cambridge University Press, Cambridge (1994) Ziller, W.: The free loop space of globally symmetric spaces. Invent. Math. 41(1), 1–22 (1977)