000 03162cam a2200517 i 4500
001 on1242021766
003 OCoLC
005 20240409130607.0
008 210305t20212021riua f b 001 0 eng
010 _a 2021004452
015 _aGBC1B7922
_2bnb
016 7 _a020272262
_2Uk
020 _a9781470456740
_qhardcover
020 _a1470456745
_qhardcover
020 _a9781470469580
_qsoftcover
020 _a1470469588
_qsoftcover
020 _z9781470465636
_qelectronic book
029 1 _aUKMGB
_b020272262
029 1 _aAU@
_b000068906547
035 _a(OCoLC)1242021766
040 _aDLC
_beng
_erda
_cDLC
042 _apcc
082 0 0 _a514.23
_bB894a
084 _a18G40
_a55N34
_a55N35
_a55P42
_a55P43
_a55Q45
_a55Q51
_a55T05
_a55T15
_2msc
090 _atop
100 1 _aBruner, R. R.
_q(Robert Ray),
_d1950-
_eauthor.
_942307
245 1 4 _aThe Adams spectral sequence for topological modular forms /
_cRobert R. Bruner, John Rognes.
264 1 _aProvidence, Rhode Island :
_bAmerican Mathematical Society,
_c[2021]
264 4 _c©2021
300 _axix, 690 pages :
_billustrations (some color) ;
_c26 cm.
336 _atext
_btxt
_2rdacontent
337 _aunmediated
_bn
_2rdamedia
338 _avolume
_bnc
_2rdacarrier
490 1 _aMathematical surveys and monographs,
_x0076-5376 ;
_vVolume 253
504 _aIncludes bibliographical references (pages 675-682) and index.
520 _a"The connective topological modular forms spectrum, tmf, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of tmf and several tmf-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degree 44, with complete proofs, except that the Adams conjecture is used without proof. Also presented are modern stable proofs of classical results which are hard to extract from the literature. Tools used in this book include a multiplicative spectral sequence generalizing a construction of Davis and Mahowald, and computer software which computes the cohomology of modules over the Steenrod algebra and products therein. Techniques from commutative algebra are used to make the calculation precise and finite. The H∞ ring structure of the sphere and of tmf are used to determine many differentials and relations."
_cProvided by publisher.
650 0 _aAlgebra, Homological.
_943544
650 0 _aHomology theory.
_943696
650 0 _aAdams spectral sequences.
_936980
697 _940
_aTopologia
700 1 _aRognes, John,
_eauthor.
_92099
830 0 _aMathematical surveys and monographs ;
_vno. 253.
_x0076-5376
_940346
942 _2ddc
_cBK
_n0
948 _hNO HOLDINGS IN P5A - 85 OTHER HOLDINGS
999 _c39846
_d39846