Ekholm, Tobias; Oancea, Alexandru Symplectic and contact differential graded algebras. (English) Zbl 1473.53097 Geom. Topol. 21, No. 4, 2161-2230 (2017). Summary: We define Hamiltonian simplex differential graded algebras (DGA) with differentials that deform the high-energy symplectic homology differential and wrapped Floer homology differential in the cases of closed and open strings in a Liouville manifold of finite type, respectively. The order-\(m\) term in the differential is induced by varying natural degree-\(m\) coproducts over an \((m-1)\)-simplex, where the operations near the boundary of the simplex are trivial. We show that the Hamiltonian simplex DGA is quasi-isomorphic to the (nonequivariant) contact homology algebra and to the Legendrian homology algebra of the ideal boundary in the closed and open string cases, respectively. Cited in 10 Documents MSC: 53D40 Symplectic aspects of Floer homology and cohomology 53D42 Symplectic field theory; contact homology 16E45 Differential graded algebras and applications (associative algebraic aspects) 18G99 Homological algebra in category theory, derived categories and functors Keywords:symplectic homology; wrapped Floer homology; contact homology; symplectic field theory PDFBibTeX XMLCite \textit{T. Ekholm} and \textit{A. Oancea}, Geom. Topol. 21, No. 4, 2161--2230 (2017; Zbl 1473.53097) Full Text: DOI arXiv References: [1] 10.1007/s11784-008-0097-y · Zbl 1171.53344 · doi:10.1007/s11784-008-0097-y [2] 10.1002/cpa.20090 · Zbl 1084.53074 · doi:10.1002/cpa.20090 [3] ; Abouzaid, Free loop spaces in geometry and topology. Free loop spaces in geometry and topology. IRMA Lect. Math. Theor. Phys., 24, 271 (2015) · Zbl 1385.53078 [4] 10.2140/gt.2010.14.627 · Zbl 1195.53106 · doi:10.2140/gt.2010.14.627 [5] 10.4310/ATMP.2014.v18.n4.a3 · Zbl 1315.81076 · doi:10.4310/ATMP.2014.v18.n4.a3 [6] 10.4310/MRL.2006.v13.n1.a6 · Zbl 1099.57023 · doi:10.4310/MRL.2006.v13.n1.a6 [7] 10.2140/gt.2012.16.301 · Zbl 1322.53080 · doi:10.2140/gt.2012.16.301 [8] 10.2140/gt.2003.7.799 · Zbl 1131.53312 · doi:10.2140/gt.2003.7.799 [9] 10.1007/s00209-004-0656-x · Zbl 1060.53080 · doi:10.1007/s00209-004-0656-x [10] 10.1007/s00222-008-0159-1 · Zbl 1167.53071 · doi:10.1007/s00222-008-0159-1 [11] 10.1215/00127094-2008-062 · Zbl 1158.53067 · doi:10.1215/00127094-2008-062 [12] 10.1093/imrn/rnw029 · Zbl 1405.53123 · doi:10.1093/imrn/rnw029 [13] 10.4310/JSG.2010.v8.n3.a2 · Zbl 1206.53083 · doi:10.4310/JSG.2010.v8.n3.a2 [14] 10.1090/coll/059 · doi:10.1090/coll/059 [15] 10.1007/PL00004267 · doi:10.1007/PL00004267 [16] 10.4171/JEMS/126 · Zbl 1154.57020 · doi:10.4171/JEMS/126 [17] 10.1007/978-0-8176-8277-4_6 · Zbl 1254.57024 · doi:10.1007/978-0-8176-8277-4_6 [18] 10.2140/gt.2013.17.975 · Zbl 1267.53095 · doi:10.2140/gt.2013.17.975 [19] 10.1142/S0129167X05002941 · Zbl 1076.53099 · doi:10.1142/S0129167X05002941 [20] 10.1090/S0002-9947-07-04337-1 · Zbl 1119.53051 · doi:10.1090/S0002-9947-07-04337-1 [21] 10.4171/JEMS/650 · Zbl 1357.57044 · doi:10.4171/JEMS/650 [22] 10.1007/s00208-013-0958-6 · Zbl 1287.53068 · doi:10.1007/s00208-013-0958-6 [23] 10.1007/978-3-0346-0425-3_4 · doi:10.1007/978-3-0346-0425-3_4 [24] ; Fukaya, Lagrangian intersection Floer theory : anomaly and obstruction. Lagrangian intersection Floer theory : anomaly and obstruction. AMS/IP Studies in Advanced Mathematics, 46 (2009) · Zbl 1181.53002 [25] 10.1215/00127094-2009-049 · Zbl 1181.53036 · doi:10.1215/00127094-2009-049 [26] 10.3934/dcds.2010.28.665 · Zbl 1211.53099 · doi:10.3934/dcds.2010.28.665 [27] 10.1007/BF02103769 · Zbl 0844.57039 · doi:10.1007/BF02103769 [28] 10.1090/coll/052 · doi:10.1090/coll/052 [29] 10.1215/S0012-7094-08-14125-0 · Zbl 1145.57010 · doi:10.1215/S0012-7094-08-14125-0 [30] 10.2140/gt.2016.20.779 · Zbl 1342.53109 · doi:10.2140/gt.2016.20.779 [31] 10.1112/jtopol/jts038 · Zbl 1298.53093 · doi:10.1112/jtopol/jts038 [32] 10.1016/0040-9383(93)90052-W · Zbl 0798.58018 · doi:10.1016/0040-9383(93)90052-W [33] 10.1007/s00039-006-0577-4 · Zbl 1118.53056 · doi:10.1007/s00039-006-0577-4 [34] ; Seidel, Current developments in mathematics, 2006, 211 (2008) · Zbl 1165.57020 [35] 10.4171/063 · Zbl 1159.53001 · doi:10.4171/063 [36] 10.1007/s000390050106 · Zbl 0954.57015 · doi:10.1007/s000390050106 [37] 10.7146/math.scand.a-23687 · Zbl 1354.58032 · doi:10.7146/math.scand.a-23687 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.